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arXiv · 1708.02414

Strong geodetic problem on Cartesian products of graphs

Vesna Iršič·Sandi Klavžar
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Abstract

The strong geodetic problem is a recent variation of the geodetic problem. For a graph $G$, its strong geodetic number ${\rm sg}(G)$ is the cardinality of a smallest vertex subset $S$, such that each vertex of $G$ lies on a fixed shortest path between a pair of vertices from $S$. In this paper, the strong geodetic problem is studied on the Cartesian product of graphs. A general upper bound for ${\rm sg}(G \,\square\, H)$ is determined, as well as exact values for $K_m \,\square\, K_n$, $K_{1, k} \,\square\, P_l$, and certain prisms. Connections between the strong geodetic number of a graph and its subgraphs are also discussed.

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Vesna Iršič, Sandi Klavžar. 2017-08-08. Strong geodetic problem on Cartesian products of graphs. https://arxiv.org/abs/1708.02414

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