Further Results on Odd Harmonious Labeling of Graphs

Abstract

Liang and Bai proposed the notion of odd harmonious labeling of a graph in 2009. Since then, numerous papers have explored this topic. This study adds some new results to the existing literature. First, we provide a sufficient condition for an Eulerian graph to be an odd harmonious graph, which enhances the result from 2014. Furthermore, we identify several new classes of graphs that exhibit odd harmonious properties.

Keywords: disjoint union of graphs; odd harmonious labeling; path union of graphs; splitting graph; subdivided shell flower graph;
vertex union of graphs.

2010 Mathematics Subject Classification. 26A25; 26A35