let $g$ be a connected graph of order $3$ or more and $c:e(g)rightarrowmathbb{z}_k$‎ ‎($kge 2$) a $k$-edge coloring of $g$ where adjacent edges may be colored the same‎. ‎the color sum $s(v)$ of a vertex $v$ of $g$ is the sum in $mathbb{z}_k$ of the colors of the edges incident with $v.$ the $k$-edge coloring $c$ is a modular $k$-edge coloring of $g$ if $s(u)ne s(v)$ in $mathbb{z}_k$ for all pa...

The corona product G ◦ H of two graphs G and H is obtained by taking one copy of G and |V (G)| copies of H; and by joining each vertex of the i-th copy of H to the i-th vertex of G, where 1 ≤ i ≤ |V (G)|. In this paper, exact formulas for the eccentric distance sum and the edge revised Szeged indices of the corona product of graphs are presented. We also study the conditions under which the cor...

Let $G$ be a simple connected graph. In this paper, Szeged dimension and PI$_v$ dimension of graph $G$ are introduced. It is proved that if $G$ is a graph of Szeged dimension $1$ then line graph of $G$ is 2-connected. The dimensions of five composite graphs: sum, corona, composition, disjunction and symmetric difference with strongly regular components is computed. Also explicit formulas of Sze...

function f: G  , with this property that f(G1) = f(G2) if G1 and G2 are isomorphic. There are several vertex distance-based and degree-based indices which introduced to analyze the chemical properties of molecule graph. For instance: Wiener index, PI index, Szeged index, geometric-arithmetic index, atom-bond connectivity index and general sum connectivity index are introduced to test the perf...

The Szeged index (Sz) is a recently proposed1q2 structural descriptor, based on the distances of the vertices of the molecular graph. In order to be able to study the properties of this novel topological index it would be advantageous to possess an easy method for its calculation. The calculation of Sz directly from its definition (see below) is quite cumbersome, especially in the case of large...