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RADIO LABELING AND RADIO NUMBER FOR GENERALIZED CATERPILLAR GRAPHS
NAZEER, SAIMA,KHAN, M. SAQIB,KOUSAR, IMRANA,NAZEER, WAQAS The Korean Society for Computational and Applied M 2016 Journal of applied mathematics & informatics Vol.34 No.5
A Radio labeling of the graph G is a function g from the vertex set V (G) of G to ℤ<sup>+</sup> such that |g(u) - g(v)| ≥ diam(G) + 1 - d<sub>G</sub>(u, v), where diam(G) and d(u, v) are diameter and distance between u and v in graph G respectively. The radio number rn(G) of G is the smallest number k such that G has radio labeling with max{g(v) : v ∈ V(G)} = k. We investigate radio number for some families of generalized caterpillar graphs.
Radio labeling and Radio Number For Generalized Caterpillar Graphs
Saima Nazeer,M. Saqib Khan,Imrana Kausar,Waqas Nazeer 한국전산응용수학회 2016 Journal of applied mathematics & informatics Vol.34 No.5
A Radio labeling of the graph $G$ is a function $g$ from the vertex set $V(G)$ of $G$ to $\mathbb{Z}^{+}$ such that $|g(u)-g(v)|\geq\text{diam}(G)+1-d_G(u,v)$, where diam$(G)$ and $d(u,v)$ are diameter and distance between $u$ and $v$ in graph $G$ respectively. The radio number rn$(G)$ of $G$ is the smallest number $k$ such that $G$ has radio labeling with max$\{g(v):v\in V(G)\}=k$. We investigate radio number for some families of generalized caterpillar graphs.