Some Results on Harmonic Graphs

A graph G is de ned to be harmonic if there is a constantλ (necessarily a natural number) such that, for every vertex v, the sum of the degrees of the neighbors of v equals λdG(v) where dG(v) is the degree of v. In this paper, we investigate the e ects of some operations on harmonic graphs. Here, we present some methods to construct new harmonic graphs from existing ones. Among other results it is shown that complement of a harmonic graph is harmonic if and only if it is a regular graph.