Abstract

In a graph $G=(V,E)$, a set $S\subseteq V(G)$ is 2-packing if $N[u]\cap N[v]=\phi$ for every $u,v\in S$, and $S$ is called open packing if $N(u)\cap N(v)=\phi$ for every $u,v\in S$. An open packing set $S$ is an outer-connected open packing set if either $S=V(G)$ or $\left\langle V-S \right\rangle$ is connected. The largest cardinalities of 2-packing, open packing, and outer-connected open packing in $G$ are respectively called the 2-packing number $(\rho)$, the open packing number $(\rho^o)$, and the outer-connected open packing number $(\rho_{oc}^o)$ of a graph $G$. In this paper, we compute these numbers for the generalized Jahangir graphs.

Keywords and Phrases

Packing number, 2-packing number, open packing number, outer-connected open packing number, Jahangir graph, generalized Jahangir graph.

A.M.S. subject classification

05C70.

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