On P2 ⋄ Pn-supermagic labeling of edge corona product of cycle and path graph

Abstract

A simple graph G = (V, E) admits a H-covering, where H is subgraph of G, if every edge in E belongs to a subgraph of G isomorphic to H. Graph G is H-magic if there is a total labeling , such that each subgraph of G isomorphic to H and satisfying where m(f) is a constant magic sum. Additionaly, G admits H-supermagic if . The edge corona of Cn and Pn is defined as the graph obtained by taking one copy of Cn and n copies of Pn, and then joining two end-vertices of the i-th edge of Cn to every vertex in the i-th copy of Pn. This research aim is to find H-supermagic covering on an edge corona product of cycle and path graph where H is . We use k-balanced multiset to solve our reserarch. Here, we find that an edge corona product of cycle and path graph is supermagic for n > 3.