Nonmedian direct products of graphs with loops.

zbMATH Open1363.05215arXiv1102.4634MaRDI QIDQ2823209

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Publication date: 6 October 2016

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Abstract: A emph{median graph} is a connected graph in which, for every three vertices, there exists a unique vertex $m$ lying on the geodesic between any two of the given vertices. We show that the only median graphs of the direct product $GimesH$ are formed when $G=P_k$, for any integer $kgeq3$ and $H=P_l$, for any integer $lgeq2$, with a loop at an end vertex, where the direct product is taken over all connected graphs $G$ on at least three vertices or at least two vertices with at least one loop, and connected graphs $H$ with at least one loop.

Full work available at URL: https://arxiv.org/abs/1102.4634

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