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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)
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)
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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