www.ejgta.org Electronic Journal of Graph Theory and Applications 6 (2) (2018), 258–268 Some diameter notions in lexicographic prod- uct of graphs Chithra M R a,b , Manju K. Menon c , A. Vijayakumar a a Department of Mathematics, Cochin University of Science and Technology, India b Current Affiliation: Department of Mathematics, Amrita School of Arts and Sciences, Kochi, Amrita Vishwa Vidyapeetham, India c Department of Mathematics, St. Paul’s College, India chithramohanr@gmail.com, manjumenonk@gmail.com, vambat@gmail.com Abstract Many graphs such as hypercubes, star graphs, pancake graphs, grids, tori etc are known to be good interconnection network topologies. In any network topology, the vertices represent the processors and the edges represent links between the processors. Two most important criteria - efficiency and reliability of network models - can be studied with the help of graph theoretical techniques. The lexicographic product is a well studied graph product. The distance notions such as various diameters of a graph help to analyze the efficiency of any interconnection network. In this paper, we study some distance notions such as wide diameter, diameter variability and diameter vulnerability of lexicographic products that could be used in the design of interconnection networks. Keywords: lexicographic product, wide diameter, diameter vulnerability, fault diameter, diameter variability Mathematics Subject Classification : 05C12, 05C76, 05C99 DOI: 10.5614/ejgta.2018.6.2.6 1. Introduction The processors of a parallel and distributed system and the connections between the processors can be represented as an interconnection network. The topological structure of an interconnection Received: 19 October 2017, Revised: 6 May 2018, Accepted: 10 June 2018. 258