M. Ghorbani
Department of mathematics, Shahid Rajaee Teacher Training University
[ 1 ] - On the eigenvalues of some matrices based on vertex degree
The aim of this paper is to compute some bounds of forgotten index and then we present spectral properties of this index. In continuing, we define a new version of energy namely ISI energy corresponded to the ISI index and then we determine some bounds for it.
[ 2 ] - On the forgotten topological index
The forgotten topological index is defined as sum of third power of degrees. In this paper, we compute some properties of forgotten index and then we determine it for some classes of product graphs.
[ 3 ] - On the Mark and Markaracter Tables of Finite Groups
Let G be a finite group and C(G) be the family of representative conjugacy classes of subgroups of G. The matrix whose H,K-entry is the number of fixed points of the set G/K under the action of H is called the table of marks of G where H,K run through all elements in C(G). Shinsaku Fujita for the first time introduced the term “markaracter” to discuss marks for permutation representati...
[ 4 ] - Relation Between Wiener, Szeged and Detour Indices
In theoretical chemistry, molecular structure descriptors are used to compute properties of chemical compounds. Among them Wiener, Szeged and detour indices play significant roles in anticipating chemical phenomena. In the present paper, we study these topological indices with respect to their difference number.
[ 5 ] - Computing Multiplicative Zagreb Indices with Respect to Chromatic and Clique Numbers
The chromatic number of a graph G, denoted by χ(G), is the minimum number of colors such that G can be colored with these colors in such a way that no two adjacent vertices have the same color. A clique in a graph is a set of mutually adjacent vertices. The maximum size of a clique in a graph G is called the clique number of G. The Turán graph Tn(k) is a complete k-partite graph whose partition...
[ 7 ] - On the energy of non-commuting graphs
For given non-abelian group G, the non-commuting (NC)-graph $Gamma(G)$ is a graph with the vertex set $G$ $Z(G)$ and two distinct vertices $x, yin V(Gamma)$ are adjacent whenever $xy neq yx$. The aim of this paper is to compute the spectra of some well-known NC-graphs.
[ 8 ] - Normalized laplacian spectrum of two new types of join graphs
Let $G$ be a graph without an isolated vertex, the normalized Laplacian matrix $tilde{mathcal{L}}(G)$ is defined as $tilde{mathcal{L}}(G)=mathcal{D}^{-frac{1}{2}}mathcal{L}(G)mathcal{D}^{-frac{1}{2}}$, where $mathcal{D}$ is a diagonal matrix whose entries are degree of vertices of $G$. The eigenvalues of $tilde{mathcal{L}}(G)$ are called as the normalized Laplacian eigenva...
[ 9 ] - ON THE SPECTRUM OF DERANGEMENT GRAPHS OF ORDER A PRODUCT OF THREE PRIMES
A permutation with no fixed points is called a derangement.The subset $mathcal{D}$ of a permutation group is derangement if all elements of $mathcal{D}$ are derangement.Let $G$ be a permutation group, a derangementgraph is one with vertex set $G$ and derangement set $mathcal{D}$ as connecting set. In this paper, we determine the spectrum of derangement graphs of order a product of three primes.
[ 10 ] - COMPUTING THE EIGENVALUES OF CAYLEY GRAPHS OF ORDER p2q
A graph is called symmetric if its full automorphism group acts transitively on the set of arcs. The Cayley graph $Gamma=Cay(G,S)$ on group $G$ is said to be normal symmetric if $N_A(R(G))=R(G)rtimes Aut(G,S)$ acts transitively on the set of arcs of $Gamma$. In this paper, we classify all connected tetravalent normal symmetric Cayley graphs of order $p^2q$ where $p>q$ are prime numbers.
[ 11 ] - On the Graovac-Ghorbani index
For the edge e = uv of a graph G, let nu = n(u|G) be the number of vertices of G lying closer to the vertex u than to the vertex v and nv= n(v|G) can be defined simailarly. Then the ABCGG index of G is defined as ABC...
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