The Perfect Roman Domination Number of the Cartesian Product of Some Graphs

Ahlam Almulhim, Abolape Deborah Akwu, Bana Al Subaiei and Akbar Ali

Journal of Mathematics, 2022, vol. 2022, 1-6

Abstract: A perfect Roman dominating function on a graph G is a function f:VG⟶0,1,2 for which every vertex v with fv=0 is adjacent to exactly one neighbor u with fu=2. The weight of f is the sum of the weights of the vertices. The perfect Roman domination number of a graph G, denoted by γRpG, is the minimum weight of a perfect Roman dominating function on G. In this paper, we prove that if G is the Cartesian product of a path Pr and a path Ps, a path Pr and a cycle Cs, or a cycle Cr and a cycle Cs, where r,s>5, then γRpG≤2/3G.

Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:1957027

DOI: 10.1155/2022/1957027

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