Minimum Linear Arrangement of the Cartesian Product of Optimal Order Graph and Path

Abstract

The minimum linear arrangement of an arbitrary graph is the embedding of the vertices of the graph onto the line topology in such a way that the sum of the distances between adjacent vertices in the graph is minimized. This minimization can be attained by finding an optimal ordering of the vertex set of the graph and labeling the vertices of the line in that order. In this paper, we compute the minimum linear arrangement of the Cartesian product of certain sequentially optimal order graphs which include interconnection networks such as hypercube, folded hypercube, complete Josephus cube and locally twisted cube with path and the edge faulty counterpart of sequentially optimal order graphs.