Two General Results on Harmonious Labelings

Abstract

In this paper, we show that if \(G\) is a harmonious graph, then \((2n+1)G\) (the disjoint union of \(2n+1\) copies of \(G\)) and \(G ^{(2n+1)}\) (the graph consisting of \(2n+1\) copies of \(G\) with one fixed vertex in common) are harmonious for all \(n \geq 0\).