H-groupmagic total labelings of families of fan graphs

Abstract

In this paper, we introduce the concept of H-groupmagic total labeling of a graph G over a finite abelian group A, that is labeling of elements of graph G with the elements of A of order p + q. An H-groupmagic total labeling of a graph G over a finite abelian group A is a bijection Λ: V(G) ∪ E(G) → A such that for any subgraph H'(V',E') of G isomorphic to H, the sum (Equation presented)is equal to magic constant k'. A graph is called H-groupmagic if it admits an H-groupmagic total labeling. We determine the H-groupmagic total labelings of fan graphs over finite abelian group A ≈ ℤ3 × Zt, where t ≥ 3. We also show that disjoint union of isomorphic as well as non-isomorphic copies of fan graphs are H-groupmagic over A ≈ ℤ3 × ℤ_t. © 2018 Utilitas Mathematica Publishing Inc. All rights reserved.