Balanced rank distribution labeling of ladder graphs, complete graphs and complete bipartite graphs

Abstract

A balanced rank distribution labeling of a graph G of order n is a new kind of vertex labeling from {1, 2, 3, ..., k}(n <= k is an element of Z(+)) which leads to a balanced edge labeling of G called edge ranks. In this paper, the balanced rank distribution labeling of ladder graphs L-n/2 for even n >= 6, complete graphs K-n for n >= 3 and complete bipartite graphs K-n/2,K-n/2 for even n >= 4 have been investigated and obtained the results on balanced rank distribution number (brd(G)) for the given graphs as follows: (i) brd(L-n/2) = 3n - 15, for even n >= 12 (ii) brd(K-n ) = n, for n >= 3 (iii) brd(K-n/2,K-n/2) = n, for even n >= 4