Gholam Hossein Fath-Tabar
@kashanu.ac.ir
Facultyof Mathematical Sciences
University of Kashan
RESEARCH INTERESTS
Algebraic Graph Theory
Scopus Publications
Scopus Publications
Mahsa Arabzadeh, , Gholam Hossein Fath-Tabar, Hamid Rasoli, Abolfazl Tehranian, , , and
University Library in Kragujevac
Ali Zeydi Abdian, Ali Reza Ashrafi, Lowell W. Beineke, Mohammad Reza Oboudi, and Gholam Hossein Fath-Tabar
Union Matematica Argentina
Meysam Taheri-Dehkordi, , and Gholam Hossein Fath-Tabar
University Library in Kragujevac
Fullerenes graphs are 3-connected, 3-regular planar graphs with faces including only pentagons and hexagons. If be a graph with a perfect matching, a subgraph H of G is a nice subgraph if G-V(H) has a perfect matching. In this paper, we show that in every fullerene graph arising from smaller fullerenes via chamfer transformation, each pair of pentagons is a nice subgraph.
Fatemeh Taghvaee and Gholam Hossein Fath-Tabar
Elsevier BV
Abstract Let G σ be an oriented graph of simple graph G with the orientation σ and vertex set V ( G ) = { v 1 , v 2 , … , v n } . The skew-adjacency matrix of G σ is the { 0 , 1 , − 1 } -matrix S = S ( G σ ) = [ s i j ] , such that s i j = 1 if ( v i , v j ) is an arc in G σ , s i j = − 1 if ( v j , v i ) is an arc in G σ and s i j = 0 , otherwise. In this paper, all oriented graphs with two and three skew-eigenvalues are characterized. Also we determine the relationship between the number of skew-eigenvalues and optimum skew energy of oriented graphs.
Tomislav Došlić, Meysam Taheri-Dehkordi, and Gholam Hossein Fath-Tabar
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.
Ali Zeydi Abdian, Afshin Behmaram, and Gholam Hossein Fath-Tabar
Informa UK Limited
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 optimiza...
Fatemeh Taghvaee and Gholam Hossein Fath-Tabar
Indonesian Mathematical Society
Let $G$ be a simple graph with vertex set $V(G)=\\{v_1, v_2, \\cdots, v_n\\}$ andedge set $E(G)$.The signless Laplacian matrix of $G$ is the matrix $Q=D+A$, such that $D$ is a diagonal matrix%, indexed by the vertex set of $G$ where%$D_{ii}$ is the degree of the vertex $v_i$ and $A$ is the adjacency matrix of $G$.% where $A_{ij} = 1$ when there%is an edge from $i$ to $j$ in $G$ and $A_{ij} = 0$ otherwise.The eigenvalues of $Q$ is called the signless Laplacian eigenvalues of $G$ and denoted by $q_1$, $q_2$, $\\cdots$, $q_n$ in a graph with $n$ vertices.In this paper we characterize all trees with four and five distinct signless Laplacian eigenvalues.
S. Akbari, G. H. Fath-Tabar, and E. Ghasemian
Informa UK Limited
Abstract Let be a simple connected graph of order n. Let 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 and the set of all edges between X and Y decomposed into r disjoint perfect matchings, then, where . Also, we determine a relation between the Laplacian eigenvalues and matchings in a bipartite graph by showing that if is a bipartite graph, and , then G has a matching that saturates U.
A. Z. Abdian, G. Fath-Tabar and M. R. Moghaddam
The main aim of this study is to characterize new classes of multicone graphs which are determined by their signless Laplacian spectra. A multicone graph is defined to be the join of a clique and a regular graph. Let C and K w denote the Clebsch graph and a complete graph on w vertices, respectively. In this paper, we show that the multicone graphs K w ▽C are determined by their signless Laplacian spectrum.
Ramin Nasiri, Hamid Reza Ellahi, Gholam Hossein Fath-Tabar, and Ahmad Gholami
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.
Mehrnoosh Javarsineh and Gholam Hossein Fath-Tabar
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.
E. Ghasemian and G.H. Fath-Tabar
National Library of Serbia
Let G? be a signed graph with the underlying graph G and with sign function ? : E(G) ? {?}. In this paper, we characterize the signed graphs with two distinct eigenvalues whose underlying graphs are triangle-free. Also, we classify all 3-regular and 4-regular signed graphs whose underlying graphs are triangle-free and give their adjacency matrices as well.
Mehrnoosh Javarsineh and Gholam Fath-Tabar
National Library of Serbia
For a simple graph G, the Q-eigenvalues are the eigenvalues of the signless Laplacian matrix Q of G. A Q-eigenvalue is said to be a Q-main eigenvalue if it admits a corresponding eigenvector non orthogonal to the all-one vector, or alternatively if the sum of its component entries is non-zero. In the literature the trees, unicyclic, bicyclic and tricyclic graphs with exactly two Q-main eigenvalues have been recently identied. In this paper we continue these investigations by identifying the trees with exactly three Q-main eigenvalues, where one of them is zero.
Hamid Reza Ellahi, Gholam Hossein Fath-Tabar, Ahmad Gholami, and Ramin Nasiri
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.
R. Nasiri and G.H. Fath-Tabar
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.
M. Adabitabar Firozja, G.H. Fath-Tabar, and Z. Eslampia
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.