 On the mutual visibility in Cartesian products and triangle-free graphsSerafino Cicerone, Gabriele Di Stefano and Sandi Klavžar Applied Mathematics and Computation, 2023, vol. 438, issue C Abstract: Given a graph G=(V(G),E(G)) and a set P⊆V(G), the following concepts have been recently introduced: (i) two elements of P are mutually visible if there is a shortest path between them without further elements of P; (ii)P is a mutual-visibility set if its elements are pairwise mutually visible; (iii) the mutual-visibility number of G is the cardinality of any largest mutual-visibility set. In this work we continue to investigate about these concepts. We first focus on mutual-visibility in Cartesian products. For this purpose, too, we introduce and investigate independent mutual-visibility sets. In the very special case of the Cartesian product of two complete graphs the problem is shown to be equivalent to the well-known Zarenkiewicz’s problem. We also characterize the triangle-free graphs with the mutual-visibility number equal to 3. Keywords: Mutual-visibility set; Mutual-visibility number; Independent mutual-visibility set; Cartesian product of graphs; Zarenkiewicz’s problem; Triangle-free graph (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:438:y:2023:i:c:s0096300322006920 DOI: 10.1016/j.amc.2022.127619 Access Statistics for this article Applied Mathematics and Computation is currently edited by Theodore Simos More articles in Applied Mathematics and Computation from Elsevier |
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