﻿ G. H. Fath-Tabar

# G. H. Fath-Tabar

Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan 87317-51167, I. R. Iran

## [ 1 ] - The irregularity and total irregularity of Eulerian graphs

For a graph G, the irregularity and total irregularity of G are defined as irr(G)=∑_(uv∈E(G))〖|d_G (u)-d_G (v)|〗 and irr_t (G)=1/2 ∑_(u,v∈V(G))〖|d_G (u)-d_G (v)|〗, respectively, where d_G (u) is the degree of vertex u. In this paper, we characterize all ‎connected Eulerian graphs with the second minimum irregularity, the second and third minimum total irregularity value, respectively.

## [ 2 ] - Relationship between Coefficients of Characteristic Polynomial and Matching Polynomial of Regular Graphs and its Applications

ABSTRACT. Suppose G is a graph, A(G) its adjacency matrix and f(G, x)=x^n+a_(n-1)x^(n-1)+... is the characteristic polynomial of G. The matching polynomial of G is defined as M(G, x) = x^n-m(G,1)x^(n-2) + ... where m(G,k) is the number of k-matchings in G. In this paper, we determine the relationship between 2k-th coefficient of characteristic polynomial, a_(2k), and k-th coefficient of matchin...

## [ 3 ] - SIGNED GENERALIZED PETERSEN GRAPH AND ITS CHARACTERISTIC POLYNOMIAL

Let G^s be a signed graph, where G = (V;E) is the underlying simple graph and s : E(G) to {+, -} is the sign function on E(G). In this paper, we obtain k-th signed spectral moment and k-th signed Laplacian spectral moment of Gs together with coefﬁcients of their signed characteristic polynomial and signed Laplacian characteristic polynomial are calculated.

## [ 4 ] - The Signless Laplacian Estrada Index of Unicyclic Graphs

‎For a simple graph \$G\$‎, ‎the signless Laplacian Estrada index is defined as \$SLEE(G)=sum^{n}_{i=1}e^{q^{}_i}\$‎, ‎where \$q^{}_1‎, ‎q^{}_2‎, ‎dots‎, ‎q^{}_n\$ are the eigenvalues of the signless Laplacian matrix of \$G\$‎. ‎In this paper‎, ‎we first characterize the unicyclic graphs with the first two largest and smallest \$SLEE\$'s and then determine the unique unicyclic graph with maximum \$SLEE\$ a...

## [ 5 ] - مجموع فاصله بین رئوس گراف

Let G=(V,E) be a graph where v(G) and E(G) are vertices and edges of G, respectively. Sum of distance between vertices of graphs is called wiener invariant. In This paper, we present some proved results on the wiener invariant and some new result on the upper bound of wiener invariant of k-connected graphs.

## [ 6 ] - گرافهای هم انرژی

فرض کنید یک گراف ساده داده شده است. هر مقدار ویژه ماتریس مجاورت این گراف یک مقدار ویژه آن نامیده می شود. انرژی یک گراف عبارت است از مجموع قدرمطلق های مقادیر ویژه آن. دو گراف با انرژی یکسان گرافهای هم انرژی نامیده می شوند. این مقاله به توصیف تاریخی و شرحی از نتایج جدید در این زمینه می پردازد.

## [ 7 ] - THE SPECTRAL DETERMINATION OF THE MULTICONE GRAPHS Kw ▽ C WITH RESPECT TO THEIR SIGNLESS LAPLACIAN SPECTRA

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 ...