Radio Number for Generalized Petersen Graphs $P(n,2)$
Feige Zhang, Saima Nazeer, Mustafa Habib, Tariq Javed Zia, Zhendong Ren · IEEE Access · 2019
Let$G$be a connected graph and$d(\mu,\omega)$be the distance between any two vertices of$G$. The diameter of$G$is denoted by$diam(G)$and is equal to$\max \{d(\mu,\omega); \\ \mu,\omega \in G\}$. The radio labeling (RL) for the graph$G$is an injective function$\digamma:V(G)\rightarrow N\cup \{0\}$such that for any pair of vertices$\mu $and$\omega \,\,|\digamma (\mu)-\digamma (\omega)|\geq diam(G)-d(\mu,\omega)+1$. The span of radio labeling is the largest number in$\digamma (V)$. The radio number of$G$, denoted by$rn(G)$is the minimum span over all radio labeling of$G$. In this paper, we determine radio number for the generalized Petersen graphs,$P(n,2)$,$n=4k+2$. Further the lower bound of radio number for$P(n,2)$when$n=4k$is determined.