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.
M. R. Chithra, Menon, M. K., and .Vijayakumar, A., “Some Diameter Notions in Lexicographic Product of Graphs”, Electronic Journal of Graph Theory and Applications , vol. 6, no. 2, pp. 258–268, 2018.