Safe Sets in Some Graph Families
Klarice Shaira R. Tan, Isagani S. Cabahug, Jr.
Asian Research Journal of Mathematics · pp. 1–7 · Published 24 Jun 2022
10.9734/arjom/2022/v18i930399Abstract
For a connected simple graph G , a non-empty set \(S \subseteq V(G)\) of vertices is a safe set if, for every component \(A \text { of }\langle S\rangle_{G}\) and every component \(B \text { of }\langle V(G)-S\rangle_{G}\) adjacent to A , it holds that \(|A| \geq|B|\). The safe number denoted by s(G) of G is the minimum cardinality of a safe set G . In this paper, it examines the characterization of a safe set in complete bipartite graph. It also discusses the minimum cardinality of a safe sets of path graph and cycle graph via modulus. Moreover, this study generates the possible exact values of the safe number of the complete graph, complete bipartite graph, and star graph.
Cited by 11
Marsha Ella, L. Maceren, Isagani S. Cabahug · Far East Journal of Mathematical Sciences (FJMS) · 2026
Wendel Glenn Jumalon, Isagani S. Cabahug · European Journal of Pure and Applied Mathematics · 2025
Takaaki Fujita · International Journal of Advanced Multidisciplinary Research and Studies · 2025
Kyle Kenneth B. Ruaya, Isagani S. Cabahug, R. Eballe · Asian Research Journal of Mathematics · 2022
Marvanessa G. Dinorog, I. Jr. · Asian Research Journal of Mathematics · 2022
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