The general position number of Cartesian products involving a factor with small diameter

Jing Tian and Kexiang Xu

Applied Mathematics and Computation, 2021, vol. 403, issue C

Abstract: A vertex subset R of a graph G is called a general position set if any triple V0⊆R is non-geodesic, this is, the three elements of V0 do not lie on the same geodesic in G. The general position number (gp-number for short) gp(G) of G is the number of vertices in a largest general position set in G. In this paper we first determine some formulae for the gp-numbers of Cartesian products involving a complete graph and of the Cartesian product of a complete multipartite graph with a path, respectively. Moreover, it is proved that gp(G□H)≤n(G)+n(H)−2 for any Cartesian product G□H with equality holding if and only if G and H are both generalized complete graphs, that is, a special class of graphs with diameters at most 2. Finally several open problems are proposed on the gp-numbers of Cartesian products.

Keywords: General position set; Cartesian product; General position number (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:403:y:2021:i:c:s0096300321002964

DOI: 10.1016/j.amc.2021.126206

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