Department of Humanities and Applied sciencesDwarkadas J. Sanghvi College of Engineering, Vile Parle (West), Mumbai, MaharashtraIndia, E-mail: smitasj1@gmail.com
Online Published on 28 December, 2021.
A labeling of a graph is a mapping that carries some set of graph elements i.e. vertices or edges or both into numbers (usually positive integers). An edge-covering of G is a family of subgraphs H1, H2, Ht such that each edge of E(G) belongs to at least one of the sub graphs Hi, i = 1, 2, …,t.
If every subgraph Hi is isomorphic to a given graph H then G is said to admit an H-covering.
In 2009, G. Sethuraman [8] has introduced concept of arbitrary super- subdivision of graph and posed a problem of labeling of it. As in su- per subdivision of cycles obvious sub graphs are seen, it generated a curiosity to study if super sub divisions of cycles admit H covering. This inspiration lead me to check even further if they can be labeled using (Super)(a, d) - H- anti magic total labeling. We prove that Super subdivision of cycle is (Super)(a, d) - H-anti magic total graph.
AMS subject classification: 05C78
Cycle, Subdivision of graphs, Super sub division of graphs, Weight of a subgraph, Edge-covering, Total labeling f of G, (a, d)-H- anti magic labeling, Super(a, d) -H - antimagic total labeling
