Harmonious labeling for the corona graphs of small complete graph

Abstract

Supposed G be a simple graph with a set of vertices (G), set of edges E(G), with | E(G)| = q. A graph G is a harmonious graph if there is an injective function f*: (G) → ℤq, such that the induced function f*: E (G) → ℤq defined by f*(xy) = f(x) + f(y), ∀xy ∈ E(G) is a bijective function. The function f is called harmonious labeling of G. It was known that a complete graph Kn is harmonious only for n ≤ 4 In this paper, we investigate the existence of harmonious labeling of the graphs from the corona operation between a complete graph K4 and Kn Kn¯, and also between K5 and Kn¯