V J Kaneria, H P Chudasama and P P Andharia
Absolute mean graceful labeling
|PUBLISHED DATE||September, 2018|
|PUBLISHER||The Author(s) 2018. This article is published with open access at www.chitkara.edu.in/publications.|
Present paper aims to focus on absolute mean graceful labeling in path union of various graphs. We proved path union of graphs like tree, path Pn, cycle Cn, complete bipartite graph Km, n, grid graph PM × Pn, step grid graph Stn and double step grid graph DStn are absolute mean graceful graphs.
Throughout present paper, we shall acknowledge G = (p, q), a finite, simple and undirected graph with V(G)-vertex set having p vertices and E(G) -edge set having q edges. For a graph G = (V, E), a function with domain V or E or V ∪ E is known as a graph labeling for G. Graceful labeling of a graph G is popular concept firstly established by Alexander (Rosa 1967). The name graceful labeling was given by (Golomb 1972) which was earlier familiar as β-valuation. Kaneria, Makadia and Meghapara (Kaneria 2015) proved graceful labeling for grid related graph. Kaneria and Makadia (Kaneria 2015) prooved graceful labeling for double step grid graph. All path graphs Pn, cycle Cn and complete bipartite graph Km, n were proved graceful graphs in the early researches in study of graceful lageling. Kaneria and Chudasama (Kaneria 2017) introduced absolute mean graceful labeling and proved that it holds true for this new labeling. Current paper is to study the same labeling for path union of finite number of copies of above mentioned graphs and enhances wide scope of operations on such graphs consisting absolute mean graceful labeling. For comprehensive learning of graph labeling, we refereed Gallian (Gallian 2011).
|ISSN||Print: 2278-9561, Online: 2278-957X|