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Facultyof Mathematical Sciences

University of Kashan

Algebraic Graph Theory

44

Scopus Publications

- The number of the skew-eigenvalues of digraphs and their relationship with optimum skew energy

Fatemeh Taghvaee and Gholam Hossein Fath-Tabar

Linear Algebra and Its Applications, ISSN: 00243795, Volume: 605, Pages: 190-205, Published: 15 November 2020 Elsevier BV - Packing stars in fullerenes

Tomislav Došlić, Meysam Taheri-Dehkordi, and Gholam Hossein Fath-Tabar

Journal of Mathematical Chemistry, ISSN: 02599791, eISSN: 15728897, Pages: 2223-2244, Published: 1 November 2020 Springer Science and Business Media LLC

A perfect star packing in a graph G is a spanning subgraph of G whose every component is isomorphic to the star graph K1,3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$K_{1,3}$$\end{document}. We investigate which fullerene graphs allow such packings. We also consider generalized fullerene graphs and packings of other graphs into classical and generalized fullerenes. Several open problems are listed. - Graphs determined by signless Laplacian spectra

Ali Zeydi Abdian, Afshin Behmaram, and Gholam Hossein Fath-Tabar

AKCE International Journal of Graphs and Combinatorics, ISSN: 09728600, Pages: 45-50, Published: 2 January 2020 Elsevier BV

Abstract In the past decades, graphs that are determined by their spectrum have received more attention, since they have been applied to several fields, such as randomized algorithms, combinatorial optimization problems and machine learning. An important part of spectral graph theory is devoted to determining whether given graphs or classes of graphs are determined by their spectra or not. So, finding and introducing any class of graphs which are determined by their spectra can be an interesting and important problem. A graph is said to be D Q S if there is no other non-isomorphic graph with the same signless Laplacian spectrum. For a D Q S graph G , we show that G ∪ r K 1 ∪ s K 2 is D Q S under certain conditions, where r , s are natural numbers and K 1 and K 2 denote the complete graphs on one vertex and two vertices, respectively. Applying these results, some D Q S graphs with independent edges and isolated vertices are obtained. - An inequality using perfect matchings and Laplacian spread of a graph

S. Akbari, G. H. Fath-Tabar, and E. Ghasemian

Linear and Multilinear Algebra, ISSN: 03081087, eISSN: 15635139, Pages: 442-447, Published: 4 March 2019 Informa UK Limited

AbstractLet G=(V,E) be a simple connected graph of order n. Let 0=μ1(G)≤μ2(G)≤⋯≤μn(G) be the Laplacian eigenvalues of G. In this paper, we show that if X and Y are two subsets of vertices of G such that |X|=|Y| and the set of all edges between X and Y decomposed into r disjoint perfect matchings, then, 2r-LS(G)2μ2(G)≤|X|n≤2r+LS(G)2μn(G), where LS(G)=μn(G)-μ2(G) . Also, we determine a relation between the Laplacian eigenvalues and matchings in a bipartite graph by showing that if G=(U,W) is a bipartite graph, |W|≥9|U| and μn(G)≤5μ2(G) , then G has a matching that saturates U. - The spectral determination of the multicone graphs K
w ▽ c with respect to their signless Laplacian spectra

Journal of Algebraic Systems, eISSN: 2345511X, Pages: 131-141, Published: 2019 - Extremely irregular unicyclic graphs

Kragujevac Journal of Mathematics, ISSN: 14509628, eISSN: 24063045, Pages: 281-292, Published: 2019 - Some new upper bounds on the wiener and edge weiner index of k-Connected graphs

Ars Combinatoria, ISSN: 03817032, Volume: 136, Pages: 335-339, Published: January 2018 - On maximum signless Laplacian Estrada index of graphs with given parameters II

Ramin Nasiri, Hamid Reza Ellahi, Gholam Hossein Fath-Tabar, and Ahmad Gholami

Electronic Journal of Graph Theory and Applications, ISSN: 23382287, Pages: 190-200, Published: 2018 The Institute for Research and Community Services (LPPM) ITB

Recently Ayyaswamy [1] have introduced a novel concept of the signless Laplacian Estrada index (after here $SLEE$) associated with a graph $G$. After works, we have identified the unique graph with maximum $SLEE$ with a given parameter such as: number of cut vertices, (vertex) connectivity and edge connectivity. In this paper we continue out characterization for two further parameters; diameter and number of cut vertices. - Unicyclic and bicyclic graphs with exactly three Q-main eigenvalues

Mehrnoosh Javarsineh and Gholam Hossein Fath-Tabar

Applied Mathematics and Computation, ISSN: 00963003, Volume: 315, Pages: 603-614, Published: 15 December 2017 Elsevier BV

Abstract Finding all the graphs with a certain number of Q -main eigenvalues is an algebraic graph theory problem that scientists have sought to answer it for many years. The purpose of this research is finding relationships between the algebraic properties of a signless Laplacian matrix of a graph and the other properties of that graph. In order to achieve this, we choose to characterize all the unicyclic and bicyclic graphs with exactly three distinct Q -main eigenvalues, one of which is zero. - On signed graphs with two distinct eigenvalues

E. Ghasemian and G.H. Fath-Tabar

Filomat, ISSN: 03545180, Pages: 6393-6400, Published: 2017 National Library of Serbia - On graphs with exactly three Q-main eigenvalues

Mehrnoosh Javarsineh and Gholam Fath-Tabar

Filomat, ISSN: 03545180, Pages: 1803-1812, Published: 2017 National Library of Serbia - The signless Laplacian Estrada index of tricyclic graphs

Australasian Journal of Combinatorics, ISSN: 10344942, eISSN: 22023518, Pages: 259-270, Published: 2017 - Resolvent Estrada and signless Laplacian Estrada indices of graphs

Match, ISSN: 03406253, Pages: 157-176, Published: 2017 - On maximum signless Laplacian Estrada index of graphs with given parameters

Hamid Reza Ellahi, Gholam Hossein Fath-Tabar, Ahmad Gholami, and Ramin Nasiri

Ars Mathematica Contemporanea, ISSN: 18553966, eISSN: 18553974, Pages: 381-389, Published: 2016 University of Primorska Press

For a simple graph G on n vertices, the signless Laplacian Estrada index is defined as S L E E ( G ) = ∑ i = 1 n e q i , where q 1 , q 2 , …, q n are the eigenvalues of the signless Laplacian matrix of G . In this paper, the unique graph on n vertices with maximum signless Laplacian Estrada index is determined among graphs with given number of cut edges, pendent vertices, (vertex) connectivity and edge connectivity, respectively. - The Second Minimum of the Irregularity of Graphs

R. Nasiri and G.H. Fath-Tabar

Electronic Notes in Discrete Mathematics, eISSN: 15710653, Pages: 133-140, Published: 2014 Elsevier BV

Abstract For a graph G , Albertson [M. O. Albertson, The irregularity of a graph, Ars Comb., 46 (1997), 219-225] has defined the irregularity of G as i r r ( G ) = ∑ x y ∈ E ( G ) | d G ( x ) − d G ( y ) | where d G ( u ) is the degree of vertex u . Recently, this graph invariant gained interest in chemical graph theory. In this work, we present some new results on the second minimum of the irregularity of graphs. - Computing chemical properties of molecules by graphs

Optoelectronics and Advanced Materials, Rapid Communications, ISSN: 18426573, eISSN: 20653824, Issue: 5-6, Pages: 439-442, Published: 2013 - Some relations between the second ga index, (Sz)
-1 Index, and (Sz)-1/2 -Index of Graphs

Match, ISSN: 03406253, Pages: 495-504, Published: 2012 - Some topological indices of an infinite 1,3-adamantane array

Studia Universitatis Babes-Bolyai Chemia, ISSN: 12247154, Pages: 151-156, Published: 2012 - The similarity measure of generalized fuzzy numbers based on interval distance

M. Adabitabar Firozja, G.H. Fath-Tabar, and Z. Eslampia

Applied Mathematics Letters, ISSN: 08939659, Pages: 1528-1534, Published: October 2012 Elsevier BV

Abstract In this paper, we proposed a new interval distance of two fuzzy numbers that satisfy on metric properties. Also, this metric distance satisfies on some of the other properties. Then, we used this metric for similarity measure. Finality, we tested with some examples. - On vertex matching polynomial of graphs

Ars Combinatoria, ISSN: 03817032, Volume: 104, Pages: 375-384, Published: April 2012 - Spectral properties of fullerenes

G. H. Fath-Tabar, A. R. Ashrafi, and D. Stevanović

Journal of Computational and Theoretical Nanoscience, ISSN: 15461955, eISSN: 15461963, Pages: 327-329, Published: March 2012 American Scientific Publishers

Since the discovery of the fullerenes in 1985 by Kroto et al.1 the fullerenes have been the object of interest of scientists all over the world. A planar graph is graph which can be drawn in the plane such that the edges do not cross. A fullerene graph is a planar 3-regular graph with only pentagonal and hexagonal faces. An IPR fullerene is a fullerene in which no two pentagons share an edge. From Euler’s theorem, it is straightforward to show that a fullerene molecule with n carbon atoms, Cn, has exactly 12 pentagons and n/2−10 hexagons.2–4 In this paper, the word graph refers to a finite, undirected graph without loops and multiple edges. Let G be a graph and v1 vn be the set of all vertices of G. The adjacency matrix of G is a 0–1 matrix A G = aij , where aij is the number of edges connecting vi and vj . A walk in a graph is a sequence of vertices such that any two consecutive vertices are adjacent. A closed walk is a walk in which the first and the last vertex are the same. The spectrum of a graph G is the set of eigenvalues of A G , together with their multiplicities. A graph of order n has exactly n real eigenvalues 1 ≤ 2 · · · ≤ n. The basic properties of graph eigenvalues can be found in a highly-cited monograph by Cvetković, Doob and Sachs.5 The Estrada index EE(G) of the graph G is defined as the sum of e i , 1 ≤ i ≤ n. By Taylor’s theorem, it can also be represented in terms of series of spectral moments EE G = ∑k≥0 ∑n i=1 k i /k!. In the last ten years, the Estrada index found applications in measuring the degree - The hyper-wiener polynomial of graphs

Iranian Journal of Mathematical Sciences and Informatics, ISSN: 17354463, eISSN: 20089473, Pages: 67-74, Published: 2011 - New upper bounds for estrada index of bipartite graphs

G.H. Fath-Tabar and A.R. Ashrafi

Linear Algebra and Its Applications, ISSN: 00243795, Volume: 435, Pages: 2607-2611, Published: 15 November 2011 Elsevier BV

Abstract Suppose G is a graph and λ 1 , λ 2 , … , λ n are the eigenvalues of G . The Estrada index EE ( G ) of G is defined as the sum of e λ i , 1 ≤ i ≤ n . In this paper some new upper bounds for the Estrada index of bipartite graphs are presented. We apply our result on a ( 4 , 6 ) -fullerene to improve our bound given in an earlier paper. - On the first geometric-arithmetic index of product graphs

Utilitas Mathematica, ISSN: 03153681, Pages: 279-287, Published: November 2011 - Some inequalities for the atom-bond connectivity index of graph operations

G.H. Fath-Tabar, B. Vaez-Zadeh, A.R. Ashrafi, and A. Graovac

Discrete Applied Mathematics, ISSN: 0166218X, Volume: 159, Pages: 1323-1330, Published: 6 August 2011 Elsevier BV

The atom-bond connectivity index is a useful topological index in studying the stability of alkanes and the strain energy of cycloalkanes. In this paper some inequalities for the atom-bond connectivity index of a series of graph operations are presented. We also prove our bounds are tight. As an application, the ABC indices of C4 nanotubes and nanotori are computed. - Old and new Zagreb indices of graphs

Match, ISSN: 03406253, Pages: 79-84, Published: 2011 - Some bounds on GA
1 index of graphs

Match, ISSN: 03406253, Pages: 33-38, Published: 2011 - The Wiener, szeged, PI, vertex PI, the first and second Zagreb indices of N-branched phenylacetylenes dendrimers

Match, ISSN: 03406253, Pages: 201-208, Published: 2011 - Bounds on the Estrada index of ISR (4,6)-fullerenes

A.R. Ashrafi and G.H. Fath-Tabar

Applied Mathematics Letters, ISSN: 08939659, Pages: 337-339, Published: March 2011 Elsevier BV

Abstract Suppose G is a graph and λ 1 , λ 2 , … λ n are the eigenvalues of G . The Estrada index E E ( G ) of G is defined as the sum of the terms e λ i , 1 ≤ i ≤ n . In this work some upper and lower bounds for the Estrada index of ( 4 , 6 ) -fullerene graphs are presented. - Some bounds on balaban index of a graph

Utilitas Mathematica, ISSN: 03153681, Pages: 325-331, Published: March 2011 - Tutte polynomial of the Stoddart's poly(Ammonium) dendrimer

Optoelectronics and Advanced Materials, Rapid Communications, ISSN: 18426573, eISSN: 20653824, Pages: 96-98, Published: January 2011 - Tutte polynomial of an infinite class of nanostar dendrimers

Studia Universitatis Babes-Bolyai Chemia, ISSN: 12247154, Pages: 131-135, Published: 2010 - Some remarks on Laplacian eigenvalues and Laplacian energy of graphs

Mathematical Communications, ISSN: 13310623, Pages: 443-451, Published: December 2010 - On Estrada index of two classes of dendrimers

Studia Universitatis Babes-Bolyai Chemia, ISSN: 12247154, Pages: 97-100, Published: 2010 - On the Szeged and the Laplacian Szeged spectrum of a graph

Gholam Hossein Fath-Tabar, Tomislav Došlić, and Ali Reza Ashrafi

Linear Algebra and Its Applications, ISSN: 00243795, Volume: 433, Pages: 662-671, Published: 1 September 2010 Elsevier BV

Abstract For a given graph G its Szeged weighting is defined by w ( e ) = n u ( e ) n v ( e ) , where e = uv is an edge of G , n u ( e ) is the number of vertices of G closer to u than to v , and n v ( e ) is defined analogously. The adjacency matrix of a graph weighted in this way is called its Szeged matrix. In this paper we determine the spectra of Szeged matrices and their Laplacians for several families of graphs. We also present sharp upper and lower bounds on the eigenvalues of Szeged matrices of graphs. - Some inequalities for szeged-like topological indices of graphs

Match, ISSN: 03406253, Pages: 145-150, Published: 2010 - GA
2 index of some graph operations

G.H. Fath-Tabar, A. Hamzeh, and S. Hossein-Zadeh

Filomat, ISSN: 03545180, Pages: 21-28, Published: April 2010 National Library of Serbia - Szeged and GA
2 indices of Suzuki's Bi-branched dendrimers

Optoelectronics and Advanced Materials, Rapid Communications, ISSN: 18426573, eISSN: 20653824, Pages: 2194-2197, Published: December 2010 - Estrada index of dendrimers

Optoelectronics and Advanced Materials, Rapid Communications, ISSN: 18426573, eISSN: 20653824, Pages: 53-55, Published: January 2010 - A new geometric-arithmetic index

Gholamhossein Fath-Tabar, Boris Furtula, and Ivan Gutman

Journal of Mathematical Chemistry, ISSN: 02599791, Pages: 477-486, Published: January 2010 Springer Science and Business Media LLC

A new molecular-structure descriptor GA2, belonging to the class of geometric–arithmetic indices, is considered. It is closely related to the Szeged and vertex PI indices. The main properties of GA2 are established, including lower and upper bounds. The trees with minimum and maximum GA2 are characterized. - Note on estrada and l-estrada indices of graphs

Bulletin, Classe des Sciences Mathematiques et Naturelles, Sciences Mathematiques, ISSN: 05617332, Volume: 139, Pages: 1-16, Published: 2009 - Extremal graphs with respect to the vertex PI index

M.J. Nadjafi-Arani, G.H. Fath-Tabar, and A.R. Ashrafi

Applied Mathematics Letters, ISSN: 08939659, Pages: 1838-1840, Published: December 2009 Elsevier BV

Abstract The vertex PI index of a graph G is the sum over all edges u v ∈ E ( G ) of the number of vertices which are not equidistant to u and v . In this paper, the extremal values of this new topological index are computed. In particular, we prove that for each n -vertex graph G , n ( n − 1 ) ≤ P I v ( G ) ≤ n ⋅ ⌊ n 2 ⌋ ⋅ ⌈ n 2 ⌉ , where ⌊ x ⌋ denotes the greatest integer not exceeding x and ⌈ x ⌉ is the smallest integer not less than x . The extremal graphs with respect to the vertex PI index are also determined. - Zagreb polynomial and PI indices of some nano structures

Digest Journal of Nanomaterials and Biostructures, eISSN: 18423582, Pages: 189-191, Published: 2009 - Note on laplacian energy of graphs

Bulletin, Classe des Sciences Mathematiques et Naturelles, Sciences Mathematiques, ISSN: 05617332, Volume: 137, Pages: 1-10, Published: 2008