Paired Domination Number of Generalized Petersen Graphs \(P(n, 2)\)

Abstract

Let \(G = (V, E)\) be a simple graph. A paired-dominating set of a graph \(G\) is a dominating set whose induced subgraph contains a perfect matching. The paired domination number of a graph \(G\), denoted by \(\gamma_p(G)\), is the minimum cardinality of a paired-dominating set in \(G\). In this paper, we study the paired domination number of generalized Petersen graphs \(P(n,2)\) and prove that for any integer \(n \geq 6\), \(\gamma_p(P(n, 2)) = 2 \left\lfloor \frac{n}{3} \right\rfloor + n \pmod{3}\).