Bholanath Mandal

Scopus Publications

Eigenvector coefficients of X10Y10 dodecahedron cages belonging to Ih and C5v symmetry point groups with the use of a 5-fold axis of symmetry, followed by Kassman’s path deletion procedure
Madhusree Nag, Rajib Mondal, Bholanath Mandal
Molecular Physics, 2026
Eigenvector or molecular orbital (MO) coefficients of the X10Y10 dodecahedron cage graphs (belonging to Ih point group for X = Y and to C5v for X ≠ Y) with X, Y = B, C, N being determined using five-fold rotational symmetry followed by the Kassman’s path deletion procedures that are subsequently illustrated in determining the eigenvectors (MOs) of the smallest fullerene C20 and smallest carbon–nitrogen hetero-fullerene (C10N10). The eigenvector coefficients can be used to calculate many physicochemical properties of the respective molecules. Here obtained eigenvector coefficients of the X10Y10 (X, Y = B, C, N) dodecahedron cages are used to evaluate the π-bond orders of the bonds and π-electron densities on the atoms. The procedure is also useful in studying reaction kinetic graphs to arrive at several consequences thereof.
Degree-based topological indices and total π-electron energies of some benzenoid hydrocarbons: correlations of strain energies and bulk modulus with such indices
Swapnadeep Mondal, Bholanath Mandal
Zeitschrift Fur Naturforschung Section A Journal of Physical Sciences, 2025
Degree-based and neighbourhood degree-sum-based (or hybrid degree-based) topological indices (TIs) for some benzenoid hydrocarbons viz. linear polyacences, methylene substituated linear polyacences, cyclacenes, linear poly (p-phenylenes), methylene substituated linear poly (p-phenylenes), and cylindrical poly (p-phenylenes) with r hexagonal rings are expressed as linear functions of r. For a given system the variation of degree-based Randić and harmonic indices or that of their hybrid indices with r is quite similar while that differs with their corresponding hybrid degree-based indices. The geometric-arithmetic index is the only one among the indices for a given system which is found to remain unaffected under consideration of neighbourhood effect. Total π-electron energies for such systems have also been derived as linear functions of r from their respective eigenspectra. Although all such TIs discussed here have good linear correlations with the total π-electron energies of the respective systems but among them the geometric-arithmetic degree-based and hybrid degree-based TIs are the best to correlate total π-electron energies for such systems. The inverses of the degree-based and hybrid degree-based TIs of cyclacenes and cylindrical poly (p-phenylenes) are found to correlate excellently well with their strain energies. The good linear correlations are also found with the inverses of the TIs of linear poly (p-phenylenes) with 2–6 hexagonal rings and their respective bulk modulus.
Atom-bond-connectivity (ABC) indices of graphene sheets, zigzag single walled carbon nanotubes and single walled carbon nanotori
Soukat Ghosh, Uday Maji, Swapnadeep Mondal, Bholanath Mandal
Zeitschrift Fur Naturforschung Section A Journal of Physical Sciences, 2024
Atom-bond-connectivity (ABC) indices are obtained in analytical forms for graphene sheets, zigzag single walled carbon nanotubes (SWCNTs), and single walled carbon nanotori in terms of number of rings (r) that measures the length and the number of hexagons in between two rings (h) that dictates the width of the concerned systems. The procedures followed for ABC index have been used to obtain the expressions of augmented Zagreb and Randić indices for such systems. Logarithm of ABC indices of zigzag SWCNTs are found to correlate linearly well with the bond dissociation energies per C–C bond and the Young’s moduli of said SWCNTs with fixed number of rings (r) but varying number of hexagons (h) in between two successive rings. The plot of logarithm of ABC index versus Young’s modulus of such SWCNTs in varying both r and h simultaneously is not a straight line but fits well with the sigmoidal (Boltzmann) curve. Wiener index, one of the important distance based index, has recently been found to have similar correlations with the concerned properties of such systems. Similar plots would appear for the said properties of the zigzag SWCNTs with other degree-based indices like augmented Zagreb and Randić indices, as have been indicated from their respective expressions obtained.
Revisiting Kassman’s path deletion procedure for the eigenvector coefficients of molecular graphs
Madhusree Nag, Bholanath Mandal
Molecular Physics, 2024
Kassman’s path deletion procedure for the determination of eigenvector polynomials (EPs) and hence the eigenvector or molecular orbital (MO) coefficients of a molecular graph is revisited with required proofs and illustrations. As EPs vanish for n-fold degenerate eigenvalues, the calculation of eigenvector (MO) coefficients for such an eigenvalue requires (n-1)-th derivative of each EP. The eigenvector coefficients for other degenerate eigenvalues are then obtained by exploiting the inherent symmetry of the molecular graph. The method of symmetry-factorisation followed by the path deletion procedure makes such calculations straightforward and simple as symmetry-factorisation distributes the degenerate eigenvalues (if there are any) in the fragmented graphs and the problem of degeneracy is thus avoided in calculating the MO coefficients for the individual fragments. The procedure is illustrated with the molecular graphs having non-degenerate and degenerate eigenvalues.
Wiener indices of zigzag single walled carbon nanotubes and related nanotories
Tapanendu Ghosh, Bholanath Mandal
Chemical Physics, 2023
Dendrimer eigen-characteristics
Bholanath Mandal, Douglas J. Klein
Journal of Mathematical Chemistry, 2022
Reaction kinetic graphs of chain reactions: Solutions for their rate equations
Sukanya Mondal, Bholanath Mandal
Chemical Physics Letters, 2021
Graph theoretical exploration for the solutions of the kinetics rate equations of nonchain complex reaction networks
Sukanya Mondal, Bholanath Mandal
International Journal of Chemical Kinetics, 2021
Abstract Nonchain complex reactions involving active center, intermediate(s), by‐products, and the final product(s) are explored with the use of graph theory for solving their rate equations. Three such reaction schemes in a varying number of intermediates are solved for the concentrations of the species involved at any instant of time ( t ). Time derivatives of these solutions result in the reaction rates of the species concerned. The time functions of rates and concentrations for three successive reaction schemes are then used to generalize the respective solutions for reaction scheme having n intermediates. The rate equations are approximated in three different time regions and are found that: (i) at time t = 0, the rate of reaction of each of the intermediate(s), by‐products, and final product is zero; (ii) at t < < < τ (average life‐time of the active center and intermediate(s)), the reaction rate of an m th intermediate, an m th by‐product, or the final product bears proportionality relationship with t m ; and (iii) at t > > > τ , the reaction rate of each of the intermediates is zero whereas that for each by‐product or final product is constant and is expressed from an initial rate multiplied by the product of the probabilities of reaction of the intermediate(s) concerned.
“Pure-Polyhex” π-Networks: Topo-Combinatorics
Douglas J. Klein, Bholanath Mandal
Croatica Chemica Acta, 2021
: Structural possibilities are considered for what arguably is the most general class of connected “pure-polyhex” π -networks (of carbon atoms). These are viewed as hexagonal-network coverings ( i.e. , a tiling by hexagons) of a connected locally Euclidean surface S possibly with holes which can be simple cycles of sizes other than 6 . The surface S can curve around to connect to itself in different ways, e.g ., with handles of different sorts. This then includes ordinary benzenoids, coronoids, carbon nanotubes, bucky-tori, carbon nano-cones, carbon nano-belts, certain fullerenes & fulleroids, various benzenoid polymers, a great diversity of defected (disclinational or dislocational) graphene flakes, and many other novel pure- polyhexes. A topological classification is made, and several combinatorial conditions on chemical sub -structure counts are identified. These counts include that of “combinatorial curvature”, such as is related to curvature stresses, as also relate to the Gaussian curvatures of the embedding surface.
Sum of characteristic polynomial coefficients of cycloparaphenylene graphs as topological index
Swapnadeep Mondal, Bholanath Mandal
Molecular Physics, 2020
Algorithm for obtaining characteristic polynomial (CP) coefficients of an alternant edge-weighted cycle is used to arrive at the algorithm for that of the cycloparaphenylene (CPP) graphs in matrix product form. The algorithm gives a recursive relation in expressing the sum of the CP coefficients of a CPP in terms of that of its two immediately preceding analogues which ultimately ends up with the use of transfer matrix in an analytical form. The sum of CP coefficients, being combinatorial in nature, is found to be used as a topological index showing much similarity with Hosoya index (sum all matching polynomial coefficients), cardinality and number of Kekulé valence structures of CPP graphs compared to the Wiener index which is the distance sum of all pairs of vertices in the graph. The sum of CP coefficients has been found to model the physical properties like strain energy and diameter of CPPs that are verified by the respective excellent correlations. GRAPHICAL ABSTRACT
Huckel molecular orbital quantities of {x,y}-cyclacene graphs under next-nearest-neighbour approximations in analytical forms
Tapanendu Ghosh, Swapnadeep Mondal, Sukanya Mondal, Bholanath Mandal
Zeitschrift Fur Naturforschung Section A Journal of Physical Sciences, 2019
{X,Y}-Cyclacene Graphs with Next Nearest Neighbor Interactions
Somnath Karmakar, Bholanath Mandal
Polycyclic Aromatic Compounds, 2019
Distance numbers and Wiener indices of IPR fullerenes with formula C10(n-2) (n ≥ 8) in analytical forms
Tapanendu Ghosh, Sukanya Mondal, Swapnadeep Mondal, Bholanath Mandal
Chemical Physics Letters, 2018
Effect of surfactants on the belousov-zhabotinsky reaction with ninhydrin as organic substrate
Sukanya Mondal, Bholanath Mandal
Tenside Surfactants Detergents, 2018
Matching polynomial coefficients and the Hosoya indices of poly(p-phenylene) graphs
Tapanendu Ghosh, Sukanya Mondal, Bholanath Mandal
Molecular Physics, 2018
Procedures for obtaining characteristic polynomials of the kinetic graphs of reversible reaction networks
Sukanya Mondal, Bholanath Mandal
Bulletin of the Chemical Society of Japan, 2018
Graph invertibility and median eigenvalues
Dong Ye, Yujun Yang, Bholanath Mandal, Douglas J. Klein
Linear Algebra and Its Applications, 2017
Symmetry-adapted linear combinations for the eigenvalues and eigenvectors of reciprocal graphs
Tapanendu Ghosh, Sukanya Mondal, Somnath Karmakar, Bholanath Mandal
Molecular Physics, 2016
Eigensolutions of cyclopolyacene graphs
Somnath Karmakar, Sukanya Mondal, Bholanath Mandal
Molecular Physics, 2015
Local symmetries for molecular graphs
Match, 2015
Cardinalities of poly(p -phenylene) graphs
Piyali Ghosh, Somnath Karmakar, Bholanath Mandal
Molecular Physics, 2014
Analytical eigenspectra of alternant edge-weighted graphs of linear chains and cycles: Some applications
Piyali Ghosh, Douglas J. Klein, Bholanath Mandal
Molecular Physics, 2014
Graph theoretical analysis on the kinetic rate equations of linear chain and cyclic reaction networks
Somnath Karmakar, Bholanath Mandal
Journal of Physical Chemistry A, 2014
Formulas for the characteristic polynomial coefficients of the pendant graphs of linear chains, cycles and stars
Piyali Ghosh, Bholanath Mandal
Molecular Physics, 2014
Schematic generation of characteristic polynomials and the hosoya indices of mono- And di-substituted polymer graphs of linear chains and cycles
Journal of the Indian Chemical Society, 2014
Graph theoretical solutions for the coupled kinetic rate equations
Somnath Karmakar, Bholanath Mandal
Journal of Physical Chemistry A, 2014
Eigensolutions of dodecahedron graphs
Piyali Ghosh, Somnath Karmakar, Bholanath Mandal
Chemical Physics Letters, 2014
Characteristic polynomial followed by trigonometric identity for obtaining analytical eigenspectra of some weighted graphs of linear chains and cycles
Bholanath Mandal, Douglas J. Klein
Bulletin of the Chemical Society of Japan, 2014
Matrix product forms for the characteristic polynomial coefficients of poly(p-phenylene) graphs
Journal of the Indian Chemical Society, 2014
Use of symmetry plane fragmentation and graph squaring techniques to express the eigenspectra for some vertex-weighted graphs of linear chains and cycles in analytical form
Piyali Ghosh, Tapanendu Ghosh, Bholanath Mandal
Molecular Physics, 2011
Characteristic polynomials of alternant edge weighted linear chains with subsequent application to some linear poly (p-phenylene) graphs
Piyali Ghosh, Bholanath Mandal
Journal of Mathematical Chemistry, 2010
Algorithms to calculate the distance numbers and the Wiener indices of linear and cylindrical poly (p-phenylene) in terms of number of hexagonal rings
Saumya Basu, Piyali Ghosh, Bholanath Mandal
Molecular Physics, 2008
Eigenspectral analysis of pendant vertex- and pendant edge-weighted graphs of linear chains, cycles, and stars
Bholanath Mandal
Bulletin of the Chemical Society of Japan, 2008
Construction and studies of a new class of reciprocal trees: Interknitting of the Pascal's triangle
Amit S. Tiwary, Bholanath Mandal, Asok K. Mukherjee
Molecular Physics, 2008
Kinetic rate equations in integrated form for single-step reactions involving different types of reactant
Anamika Ray, Bholanath Mandal
Progress in Reaction Kinetics and Mechanism, 2008
Some important formulae using the concept of graphical tree
Bholanath Mandal
Chemical Physics Letters, 2006
Use of symmetry plane and subsequent subtraction for obtaining eigenspectra of some complicated graphs in analytical forms
Bholanath Mandal
Journal of Molecular Structure THEOCHEM, 2005
Construction and utilisation of planar graphs of two series of IPR fullerenes through the use of threefold rotational symmetry
Bholanath Mandal, Kakali Datta, Manas Banerjee, Asok K. Mukherjee
International Journal of Quantum Chemistry, 2005
Wiener and Hosoya indices of reciprocal graphs
B. Mandal, M. Banerjee, A. K. Mukherjee *
Molecular Physics, 2005
Graph theoretical procedure for obtaining analytical expressions of eigenspectra of linear chains and cycles with alternant vertex weights and same edge weight: Application to some complicated graphs
Bholanath Mandal
International Journal of Quantum Chemistry, 2005
Construction of characteristic polynomial of reciprocal graphs from the number of pendant vertices
Bholanath Mandal, Manas Banerjee, Asok K. Mukherjee
International Journal of Quantum Chemistry, 2005
Cardinalities of reciprocal graphs
Bholanath Mandal, Manas Banerjee, Asok K. Mukherjee
International Journal of Quantum Chemistry, 2004
Construction of planar graphs for IPR fullerenes using 5- and 6-fold rotational symmetry: Some eigenspectral analysis
Bholanath Mandal, Manas Banerjee, Asok K. Mukherjee
Physical Chemistry Chemical Physics, 2004
Study of a reaction between 1,3-dinitrobenzene and acetophenone in presence of hydroxide ion
Journal of the Indian Chemical Society, 2004
A Pascal's triangle-like approach for the determination of characteristic polynomial coefficients of reciprocal graphs
BHOLANATH MANDAL, KAKALI DATTA, ASOK K. MUKHERJEE, MANAS BANERJEE
Molecular Physics, 1999

RECENT SCHOLAR PUBLICATIONS

Eigenvector coefficients of X 10 Y 10 dodecahedron cages belonging to I h and C 5v symmetry point groups with the use of a 5-fold axis of symmetry, followed by …
M Nag, R Mondal, B Mandal
Molecular Physics 124 (2), e2502160 , 2026
2026
Degree-based topological indices and total π-electron energies of some benzenoid hydrocarbons: correlations of strain energies and bulk modulus with such indices
S Mondal, B Mandal
Zeitschrift für Naturforschung A 80 (10), 961-991 , 2025
2025
Atom-bond-connectivity (ABC) indices of graphene sheets, zigzag single walled carbon nanotubes and single walled carbon nanotori
S Ghosh, U Maji, S Mondal, B Mandal
Zeitschrift für Naturforschung A , 2024
2024
Citations: 3
Revisiting Kassman’s path deletion procedure for the eigenvector coefficients of molecular graphs
M Nag, B Mandal
Molecular Physics, e2307498 , 2024
2024
Citations: 1
Wiener indices of zigzag single walled carbon nanotubes and related nanotories
T Ghosh, B Mandal
Chemical Physics 572, 111973 , 2023
2023
Citations: 2
Dendrimer eigen-characteristics
B Mandal, DJ Klein
Journal of Mathematical Chemistry 60 (7), 1131-1162 , 2022
2022
Citations: 5
Reaction kinetic graphs of chain reactions: Solutions for their rate equations
S Mondal, B Mandal
Chemical Physics Letters 781, 138977 , 2021
2021
Citations: 4
Graph theoretical exploration for the solutions of the kinetics rate equations of nonchain complex reaction networks
S Mondal, B Mandal
International Journal of Chemical Kinetics 53 (6), 751-774 , 2021
2021
Citations: 3
“Pure-Polyhex” π-Networks: Topo-Combinatorics
DJ Klein, B Mandal
Croatica Chemica Acta 93 (4), 349-365 , 2021
2021
Citations: 1
Sum of characteristic polynomial coefficients of cycloparaphenylene graphs as topological index
S Mondal, B Mandal
Molecular Physics 118 (13), e1685693 , 2020
2020
Citations: 8
Hückel molecular orbital quantities of {X, Y}-cyclacene graphs under next-nearest-neighbour approximations in analytical forms
T Ghosh, S Mondal, S Mondal, B Mandal
Zeitschrift für Naturforschung A 74 (6), 469-488 , 2019
2019
Citations: 4
{X, Y}-Cyclacene Graphs with Next Nearest Neighbor Interactions
S Karmakar, B Mandal
Polycyclic Aromatic Compounds 39 (2), 159-171 , 2019
2019
Citations: 7
Matching polynomial coefficients and the Hosoya indices of poly (p-phenylene) graphs
T Ghosh, S Mondal, B Mandal
Molecular Physics 116 (3), 361-377 , 2018
2018
Citations: 12
Effect of Surfactants on the Belousov- Zhabotinsky Reaction with Ninhydrin as Organic Substrate
S Mondal, B Mandal
Tenside Surf. Det. 55 (3), 196-202 , 2018
2018
Distance numbers and Wiener indices of IPR fullerenes with formula C10(n-2) (n>=8) in analytical forms
T Ghosh, S Mondal, S Mondal, B Mandal
Chemical Physics Letters 701, 72-80 , 2018
2018
Citations: 4
Procedures for Obtaining Characteristic Polynomials of the Kinetic Graphs of Reversible Reaction Networks
S Mondal, B Mandal
Bulletin of the Chemical Society of Japan 91 (4), 700–709 , 2018
2018
Citations: 4
Graph Invertibility and Median Eigenvalues
D Ye, Y Yang, B Mandal, DJ Klein
Linear Algebra and its Applications 513, 304-323 , 2017
2017
Citations: 31
Symmetry-adapted linear combinations for the eigenvalues and eigenvectors of reciprocal graphs
T Ghosh, S Mondal, S Karmakar, B Mandal
Molecular Physics 114 (22), 3307-3318 , 2016
2016
Citations: 7
Eigensolutions of cyclopolyacene graphs
S Karmakar, S Mondal, B Mandal
Molecular Physics 113 (7), 719-726 , 2015
2015
Citations: 18
Local Symmetries for Molecular Graphs
DJ Klein, B Mandal
MATCH Commun. Math. Comput. Chem. 74, 247-258 , 2015
2015
Citations: 14

MOST CITED SCHOLAR PUBLICATIONS

Graph Invertibility and Median Eigenvalues
D Ye, Y Yang, B Mandal, DJ Klein
Linear Algebra and its Applications 513, 304-323 , 2017
2017
Citations: 31
Eigensolutions of cyclopolyacene graphs
S Karmakar, S Mondal, B Mandal
Molecular Physics 113 (7), 719-726 , 2015
2015
Citations: 18
Wiener and Hosoya indices of reciprocal graphs
B Mandal, M Banerjee, AK Mukherjee*
Molecular Physics 103 (19), 2665-2674 , 2005
2005
Citations: 18
Cardinalities of reciprocal graphs
B Mandal, M Banerjee, AK Mukherjee
International journal of quantum chemistry 99 (3), 119-126 , 2004
2004
Citations: 17
A Pascal's triangle-like approach for the determination of characteristic polynomial coefficients of reciprocal graphs
B Mandal, K Datta, AK Mukherjee, M Banerjee
Molecular Physics 96 (11), 1609-1611 , 1999
1999
Citations: 17
Construction of planar graphs for IPR fullerenes using 5-and 6-fold rotational symmetry: some eigenspectral analysis
B Mandal, M Banerjee, AK Mukherjee
Physical Chemistry Chemical Physics 6 (9), 2040-2043 , 2004
2004
Citations: 16
Algorithms to calculate the distance numbers and the Wiener indices of linear and cylindrical poly (p-phenylene) in terms of number of hexagonal rings
S Basu, P Ghosh, B Mandal
Molecular Physics 106 (21-23), 2507-2513 , 2008
2008
Citations: 15
Eigenspectral analysis of pendant vertex-and pendant edge-weighted graphs of linear chains, cycles, and stars
B Mandal
Bulletin of the Chemical Society of Japan 81 (8), 956-965 , 2008
2008
Citations: 15
Local Symmetries for Molecular Graphs
DJ Klein, B Mandal
MATCH Commun. Math. Comput. Chem. 74, 247-258 , 2015
2015
Citations: 14
Analytical eigenspectra of alternant edge-weighted graphs of linear chains and cycles: some applications
P Ghosh, DJ Klein, B Mandal
Molecular Physics 112 (16), 2093-2106 , 2014
2014
Citations: 14
Graph theoretical procedure for obtaining analytical expressions of eigenspectra of linear chains and cycles with alternant vertex weights and same edge weight: Application to …
B Mandal
International Journal of Quantum Chemistry 103 (2), 140-148 , 2005
2005
Citations: 13
Matching polynomial coefficients and the Hosoya indices of poly (p-phenylene) graphs
T Ghosh, S Mondal, B Mandal
Molecular Physics 116 (3), 361-377 , 2018
2018
Citations: 12
Use of symmetry plane and subsequent subtraction for obtaining eigenspectra of some complicated graphs in analytical forms
B Mandal
Journal of Molecular Structure: THEOCHEM 757 (1-3), 99-111 , 2005
2005
Citations: 12
Graph theoretical analysis on the kinetic rate equations of linear chain and cyclic reaction networks
S Karmakar, B Mandal
The Journal of Physical Chemistry A 118 (36), 7672-7682 , 2014
2014
Citations: 11
Graph theoretical solutions for the coupled kinetic rate equations
S Karmakar, B Mandal
The Journal of Physical Chemistry A 118 (7), 1155-1161 , 2014
2014
Citations: 11
Eigensolutions of dodecahedron graphs
P Ghosh, S Karmakar, B Mandal
Chemical Physics Letters 594, 41-46 , 2014
2014
Citations: 11
Characteristic polynomials of alternant edge weighted linear chains with subsequent application to some linear poly (p-phenylene) graphs
P Ghosh, B Mandal
Journal of Mathematical Chemistry 48 (4), 1069-1091 , 2010
2010
Citations: 10
Characteristic polynomial followed by trigonometric identity for obtaining analytical eigenspectra of some weighted graphs of linear chains and cycles
B Mandal, DJ Klein
Bulletin of the Chemical Society of Japan 87 (4), 491-497 , 2014
2014
Citations: 9
Sum of characteristic polynomial coefficients of cycloparaphenylene graphs as topological index
S Mondal, B Mandal
Molecular Physics 118 (13), e1685693 , 2020
2020
Citations: 8
Construction and utilisation of planar graphs of two series of IPR fullerenes through the use of threefold rotational symmetry
B Mandal, K Datta, M Banerjee, AK Mukherjee
International Journal of Quantum Chemistry 105 (3), 201-208 , 2005
2005
Citations: 8

Bholanath Mandal

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Scopus Publications

RECENT SCHOLAR PUBLICATIONS

MOST CITED SCHOLAR PUBLICATIONS