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Isometric path numbers of graphs

Jun-Jie Pan·Gerard J. Chang
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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.

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Jun-Jie Pan, Gerard J. Chang. 2003-10-21. Isometric path numbers of graphs. https://arxiv.org/abs/math/0310332

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