Journal article

Radio number of trees

D Bantva, S Vaidya, S Zhou

Electronic Notes in Discrete Mathematics | Published : 2015

Abstract

A radio labeling of a graph G is a mapping f: V(G)→{0, 1, 2, ...} such that |f(u)-f(v)|≥d+1-d(u,v) for every pair of distinct vertices u, v of G, where d and d(u,v) are the diameter of G and the distance between u and v in G, respectively. The radio number of G is the smallest integer k such that G has a radio labeling f with max{f(v):v∈V(G)}=k. We present a lower bound for the radio number of trees and a necessary and sufficient condition for this bound to be achieved. Using this condition we determine the radio number for three families of trees.

University of Melbourne Researchers

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