On the Domination Number of Generalized Petersen Graphs \(P(n, 3)\)

Abstract

Let \(G = (V(G), E(G))\) be a graph. A set \(S \subseteq V(G)\) is a dominating set if every vertex of \(V(G) – S\) is adjacent to some vertices in \(S\). The domination number \(\gamma(G)\) of \(G\) is the minimum cardinality of a dominating set of \(G\). In this paper, we study the domination number of generalized Petersen graphs \(P(n,3)\) and prove that \(\gamma(P(n,3)) = n – 2\left\lfloor \frac{n}{4} \right\rfloor (n\neq 11)\).