Some Inequalities for Szeged-Like Topological Indices of Graphs G. H. Fath-Tabar * , M. J. Nadjafi-Arani, M. Mogharrab Department of Mathematics, Faculty of Science, University of Kashan, Kashan 87317-51167, Iran A. R. Ashrafi † Department of Mathematics, Faculty of Science, University of Kashan, Kashan 87317-51167, Iran School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P.O. Box: 19395–5746, Tehran, Iran (Received January 27, 2009) Abstract The PI, vertex PI and edge Szeged index are three of most important Szeged- like topological indices introduced very recently. The aim of this paper is to present some sharp inequalities between PI, Vertex PI, Szeged and edge Szeged indices of graphs. 1 Introduction Throughout this paper we only consider finite connected graph. Let G be a graph with vertex and edge sets V (G) and E(G), respectively. As usual, the distance between the vertices u and v of G is denoted by d G (u, v)(d(u, v) for short) and it is defined as the number of edges in a shortest path connecting the vertices u and v. ∗ Corresponding author (E-mail: fathtabar@kashanu.ac.ir). † This author was in part supported by a grant from IPM (No. 87200113). MATCH Communications in Mathematical and in Computer Chemistry MATCH Commun. Math. Comput. Chem. 63 (2010) 145-150 ISSN 0340 - 6253