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Radio Number for Generalized Petersen Graphs $P(n,2)$
- Source :
- IEEE Access, Vol 7, Pp 142000-142008 (2019)
- Publication Year :
- 2019
- Publisher :
- IEEE, 2019.
-
Abstract
- 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.
Details
- Language :
- English
- ISSN :
- 21693536
- Volume :
- 7
- Database :
- Directory of Open Access Journals
- Journal :
- IEEE Access
- Publication Type :
- Academic Journal
- Accession number :
- edsdoj.2bfd4328b42646cbb51cbc4b470f4884
- Document Type :
- article
- Full Text :
- https://doi.org/10.1109/ACCESS.2019.2943835