Multi-level distance labelings for the prism related graphs $D^{p}_{n}$

Saima Nazeer, Imrana Kousar


Let $G$ be a connected graph with diameter diam$(G)$ and $d(x,y)$ denotes the distance between any two distinct vertices $x$, $y$ in $G$. A radio labeling $f$ of $G$ is an assignment of non negative integer to the vertices of $G$ satisfying $|f(x)-f(y)|\geq $diam$(G)-d(x,y)+1$. The span of a radio labeling is the maximum integer assigned to a vertex. The radio number of $G$ denoted by rn$(G)$, is the minimum possible span. In this paper, we determine the radio number for the prism related graphs, $D_{n}^{p}$ when $n=4k+2$.

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