Gholam Hossein Fath-Tabar

Verified email at kashanu.ac.ir

Facultyof Mathematical Sciences
University of Kashan



                     

http://researchid.co/fathtabar

RESEARCH INTERESTS

Algebraic Graph Theory

44

Scopus Publications

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 Kw ▽ 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 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 GA1 index of graphs
    Match, ISSN: 03406253, Pages: 33-38, 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 GA2 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