Radio labeling for some cycle related graphs
Journal: International Journal of Mathematics and Soft Computing (Vol.2, No. 2)Publication Date: 2012-07-22
Authors : S K Vaidya P L Vihol;
Page : 11-24
Keywords : Graph labeling; radio number; channel assignment;
Abstract
Let $G=(V(G),E(G))$ be a connected graph and let $d(u,v)$ denote the distance between any two vertices in $G$. The maximum distance between any pair of vertices is called the diameter of $G$ denoted by $diam(G)$. A radio labeling( or multilevel distance labeling) for $G$ is an injective function $f:V(G) longrightarrow Ncup{0}$ such that for any vertices $u$ and $v$, $|f(u)-f(v)| geq diam(G)-d(u,v)+1$. The span of $f$ is the largest number in $f(V)$. The radio number of $G$, denoted by $r_n(G)$ is the minimum span of a radio labeling of $G$. In this paper we determine upper bounds of radio numbers for cycle with chords and $n/2$-petal graph. Further the radio number is completely determined for the split graph and middle graph of cycle $C_{n}$.
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