Isometric path numbers of graphs
classification
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keywords
isometricpathgraphscompletenumbernumbersverticescartesian
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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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