The Domination Number of Generalized Petersen Graphs with a Faulty Vertex
In this paper, we investigate the domination number of generalized Petersen graphs P(n, 2) when there is a faulty vertex. Denote by $γ(P(n,2))$ the domination number of P(n,2) and $γ(P_f(n,2))$ the domination number of P(n,2) with a faulty vertex $u_f$. We show that $γ(P_f(n,2))=γ(P(n,2))-1$ when $n=5k+1$ or $5k+2$ and $γ(P_f(n,2))=γ(P(n,2))$ for the other cases.
math.GR↗