Another Look of Rings Domination in Ladder Graph
Kyle Kenneth B. Ruaya
Mathematics Department, College of Arts and Sciences, Central Mindanao University, Musuan, Maramag, Bukidnon, Philippines.
Isagani S. Cabahug, Jr.
Mathematics Department, College of Arts and Sciences, Central Mindanao University, Musuan, Maramag, Bukidnon, Philippines.
Rolito G. Eballe *
Mathematics Department, College of Arts and Sciences, Central Mindanao University, Musuan, Maramag, Bukidnon, Philippines.
*Author to whom correspondence should be addressed.
Abstract
For a nontrivial connected graph \(G\) with no isolated vertex, a nonempty subset \(D \subseteq V(G)\) is a rings dominating set if each vertex \(v \in V-D\) is adjacent to at least two vertices in \(V-D\). Thus, the dominating set \(D\) of \(V(G)\) is a rings dominating set if for all \(v \in V-D,|N(v) \cap(V-D)| \geq 2\). The cardinality of minimum rings dominating set of \(G\) is the rings domination number of \(G\), denoted by \(\gamma_{r_i}\) whereas the cardinality of maximum rings dominating set is the upper rings domination number and is denoted by \(\gamma_{r i}^{\prime}\). Here, we determine how the rings dominating set is constructed in the ladder graph with the inclusion of generated conditions for this type of domination and give new approach for its parameter.
Keywords: Rings dominating set, rings domination number, upper rings domination