Multilevel Distance Labeling for Generalized Petersen P (4k + 2, 2) related Graphs
نویسندگان
چکیده
Abstract A multilevel distance labeling of the graph G is a function f = (V (G),E(G)) on V (G) of G into N ∪ {0} so that |f(u) − f(v)| ≥ diam(G) + 1− d(u, v) for all u, v ∈ V (G). The smallest span taken over all multilevel distance labeling of G is radio number rn(G) of G. In this paper, we completely determine the radio number rn(G) of G where G is the graph obtained from generalized Petersen graph P (n, 2), where n = 4k+2 by adding new edges uivi+1 and ui+1vi i.e. V (G) = V (P (4k+2, 2)) and E(G) = E(P (4k + 2, 2)) ∪ {uivi+1, ui+1vi : 1 ≤ i ≤ 4k + 2}.
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