The radio and radio antipodal numbers of non-bipartite cubic graphs of order 2~k

摘要

Let G be a connected graph with diameter diam(G) = d, and d(x,y) denotes the distance between two distinct vertices x, y in G. A radio k- labeling of a graph G is an assignment of non negative integers to the vertices of G such that the inequality |f(x) - f(y)| ≥k+1 - d(x, y) holds for any two vertices x, y in G. The radio number is the minimum span of a radio (diam(G))-labeling of G and the radio antipodal number is the minimum span of a (diam(G) - 1)-labeling of G. In this paper, we determine the radio number and radio antipodal number of non-bipartite cubic graphs of order 2~k.