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A radio k-labeling c of a graph G is a mapping c : V (G) → Z + ∪{0} such that d(u, v)+|c(u)−c(v)| ≥ k+1 for every two distinct vertices u and v of G, where d(u, v) is the distance between any two vertices u and v of G. The span of a radio k-labeling c is denoted by sp(c) and defined as max{|c(u) − c(v)| : u, v ∈ V (G)}. The radio labeling is a radio(More)
A vertex v is a peripheral vertex in G if its eccentricity is equal to its diameter, and periphery P(G) is a subgraph of G induced by its peripheral vertices. Further, a vertex v in G is a central vertex if e(v) = rad(G), and the subgraph of G induced by its central vertices is called center C(G) of G. Average eccentricity is the sum of eccentricities of(More)
Let G be a connected graph with diameter diam () G and (,) d x y denotes the shortest distance between any two distinct vertices , xy in G. Radio labeling (multi-level distance labeling or distance labeling) of G is a one-to-one mapping : () {0} f V G Z   satisfying (,) | () () | () 1 d x y f x f y diam G     for all , () x y V G . The span of a(More)
the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 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(More)
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