Isometric path numbers of graphs
arXiv:math/0310332
Abstract
An isometric path between two vertices in a graph is a shortest path joining them. The isometric path number of , denoted by $\ip(G)$, is the minimum number of isometric paths needed to cover all vertices of . In this paper, we determine exact values of isometric path numbers of complete -partite graphs and Cartesian products of 2 or 3 complete graphs.
9 pages