Let G be a simple connected graph. A nonempty subset  is a safe dominating set if S is a dominating set of G and for every component A of  and every component B of  adjacent to A,  A safe dominating set of the smallest size in a given graph is called the safe domination set denoted as -set. The cardinality of -set is called safe domination number. In this paper, we determine sufficient conditions for the safe dominating set of a ladder graph. Moreover, we provide the upper bound of the safe domination number of such a graph.

safe dominating set, ladder graph

Received: March 6, 2024; Accepted: May 1, 2024; Published: May 11, 2024

How to cite this article: Marsha Ella L. Maceren and Isagani S. Cabahug, Jr., Safe domination in the ladder graph, Advances and Applications in Discrete Mathematics 41(4) (2024), 331-339. https://doi.org/10.17654/0974165824024

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

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