Let G be a connected graph and d(µ, ω) be the distance between any two vertices of G. The diameter of G is denoted by diam(G) and is equal to max{d(µ, ω); µ, ω ∈ G}. The radio labeling (RL) for the graph G is an injective function : V (G) → N ∪ {0} such that for any pair of vertices µ andThe span of radio labeling is the largest number in (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.INDEX TERMS Diameter, radio number, generalized Petersen graph.
The energy of a simple connected graph G is equal to the sum of the absolute value of eigenvalues of the graph G where the eigenvalue of a graph G is the eigenvalue of its adjacency matrix AG. Ultimately, scores of various graph energies have been originated. It has been shown in this paper that the different graph energies of the regular splitting graph S′G is a multiple of corresponding energy of a given graph G.
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.
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