$K$-odd sequential harmonious labeling of some graphs

Abstract

A labeling of a graph is the assigning of natural values to the vertices of the graph in some way that induces edge labels according to certain pattern. Interest in graph labeling began in 1967 when A. Rosa (On certain valuations of the vertices of a graph, Theory of Graphs, (International Symposium, Rome, July 1966), (1967), Gordon and Breach, New York and Dunod Pairs, 349-355) published his paper on graph labeling. In this paper, we prove that Ladder, Pyramid and the degree splitting of Star and Bistar graphs are $k$- odd sequential harmonious graphs.