-The Szeged index Sz is a recently introduced graph invariant, having applications in chemistry. In this paper, a formula for the Szeged index of Cartesian product graphs is obtained and some other composite graphs are considered. We also prove that for all connected graphs, Sz is greater than or equal to the sum of distances between all vertices. A conjecture concerning the maximum value of Sz...

Péter Lajkó,1 Enrico Carlon,2 Heiko Rieger,3 and Ferenc Iglói4,5 1Department of Physics, Kuwait University, P.O. Box 5969, Safat 13060, Kuwait 2Interdisciplinary Research Institute c/o IEMN, Cité Scientifique Boîte Postale 60069, F-59652 Villeneuve d’Ascq, France 3Theoretische Physik, Universität des Saarlandes, D-66041 Saarbrücken, Germany 4Research Institute for Solid State Physics and Optics...

Let $G$ be a non-abelian group and let $Z(G)$ be the center of $G$. Associate with $G$ there is agraph $Gamma_G$ as follows: Take $Gsetminus Z(G)$ as vertices of$Gamma_G$ and joint two distinct vertices $x$ and $y$ whenever$yxneq yx$. $Gamma_G$ is called the non-commuting graph of $G$. In recent years many interesting works have been done in non-commutative graph of groups. Computing the clique...

Let G be a simple graph with vertex set and edge set . The function which assigns to each pair of vertices in , the length of minimal path from to , is called the distance function between two vertices. The distance function between and edge and a vertex is where for and. , . The Wiener index of a graph is denoted by and is defined by .In general this kind of index is called a topological index...

Let G be a connected graph, nu(e) is the number of vertices of G lying closer to u and nv(e) is the number of vertices of G lying closer to v. Then the Szeged index of G is defined as the sum of nu(e)nv(e), over edges of G.. The PI index of G is a Szeged-like topological index defined as the sum of [mu(e)+ mv(e)], where mu(e) is the number of edges of G lying closer to u than to v, mv(e) is the...