H-supermagic labeling on edge coronation of some graphs with a cycle

Abstract

Let H be a graph. A simple graph G=(V(G), E(G)) admits an H-covering if every edge in E(G) belongs to some subgraphs of G that isomorphic to a given graph H. A graph G is H-magic if there exists a total labeling f: V(G) ∪ E(G) → {1, 2, …, |V(G)|+|E(G)|}, such that all subgraphs H′=(V(H′), E(H′)) of G isomorphic to H have the same weight. In this case, the weight of H′ is defined as the sum of all vertex and edge labels of graph H′ and is denoted by f (H′). Additionally, G is an H-supermagic labeling if f (V(G)) = {1, 2, …, |V(G)|}.This research aims to find an H-supermagic labeling of G, for two cases. In case one, we consider G as edge corona product of a star graph and a cycle and H as edge corona product of a path with length two and a cycle. In case two, we consider G as edge corona product of a book graph and a cycle and H as a edge corona product of a cycle with order 4 and a cycle.Let H be a graph. A simple graph G=(V(G), E(G)) admits an H-covering if every edge in E(G) belongs to some subgraphs of G that isomorphic to a given graph H. A graph G is H-magic if there exists a total labeling f: V(G) ∪ E(G) → {1, 2, …, |V(G)|+|E(G)|}, such that all subgraphs H′=(V(H′), E(H′)) of G isomorphic to H have the same weight. In this case, the weight of H′ is defined as the sum of all vertex and edge labels of graph H′ and is denoted by f (H′). Additionally, G is an H-supermagic labeling if f (V(G)) = {1, 2, …, |V(G)|}.This research aims to find an H-supermagic labeling of G, for two cases. In case one, we consider G as edge corona product of a star graph and a cycle and H as edge corona product of a path with length two and a cycle. In case two, we consider G as edge corona product of a book graph and a cycle and H as a edge corona product of a cycle with order 4 and a cycle.