Isometric path numbers of graphs

Jun-Jie Pan; Gerard J. Chang

Isometric path numbers of graphs

Combinatorics 2007-05-23 v1

Authors: Jun-Jie Pan , Gerard J. Chang

Abstract

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

Keywords

graph pebbling rainbow connection graph theory

Cite

@article{arxiv.math/0310332,
  title  = {Isometric path numbers of graphs},
  author = {Jun-Jie Pan and Gerard J. Chang},
  journal= {arXiv preprint arXiv:math/0310332},
  year   = {2007}
}

Comments

9 pages

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