Some New Perspectives on Distance Two Labeling
Samir K. VAIDYA, Devsi Bantva · International Journal of Mathematics and Soft Computing · 2013
An $L(2,1)$-labeling (or distance two labeling) of a graph $G$ is a function $f$ from the vertex set $V(G)$ to the set of nonnegative integers such that $|f(u)-f(v)|\geq2$ if $d(u,v)=1$ and $|f(u)-f(v)|\geq1$ if $d(u,v)=2$. The $L(2,1)$-labeling number $\lambda(G)$ of $G$ is the smallest number $k$ such that $G$ has an $L(2,1)$-labeling with max$\{f(v):v \in V(G)\}=k$. In this paper we find $\lambda$-number for some cacti.