## BALANCED RANK DISTRIBUTION LABELING OF LADDER GRAPHS, COMPLETE GRAPHS AND COMPLETE BIPARTITE GRAPHS

## BALANCED RANK DISTRIBUTION LABELING OF LADDER GRAPHS, COMPLETE GRAPHS AND COMPLETE BIPARTITE GRAPHS

*P. Hemalatha, S. Gokilamani*

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## 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 ∈ Z+) which leads to a balanced edge labeling of G called edge ranks. In this paper, the balanced rank distribution labeling of ladder graphs Ln/2 for even n ≥ 6, complete graphs Kn for n ≥ 3 and complete bipartite graphs Kn/2,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(Ln/2)=3n−15,forevenn≥12

(ii) brd(Kn)=n,forn≥3

(iii) brd(Kn/2,n/2) = n, for even n ≥ 4

## Keywords

Labeling of graphs, Balanced rank distribution labeling, Edge ranking, Bal- anced rank distribution number, Strongly and Weakly balanced rank distribution graphs.