H-Supermagic Labeling on Coronation of Some Classes of Graphs with a Path

Abstract

A simple graph G = (V; E) admits an H-covering if every edge in E belongs to a subgraph on G that isomorphic to H. A graph G is H-magic if there is exists a total labeling f : V (G)∪E(G) → {1, 2, …, |V|+|E|}, such that each subgraph H′ = (V′(H′); E′(H′)) on G satisfies f(H′) = ∑v∈V′ f(v) + ∑e∈E′ f(e) = m(f), where m(f) is a constant magic sum. A graph G is a H-supermagic labeling if f(V ) = {1, …, |V|} and s(f) is a constant supermagic sum. The research aims to study a H-supermagic labeling on corona product of a star graph with a path and a wheel graph with a path. We prove that the corona product of a star graph with a path Sn ⊙ Pm is a Um,2-supermagic for m is odd or m, n are even and m ≥ 3 and the corona product of a wheel graph with a path Wn ⊙ Pm is a C3 ⊙ Pm-supermagic for m ≥ 3.