Document Type : Research Paper

Authors

• G. Marimuthu ¹
• S. Stalin Kumar ²

¹ Department of Mathematics, The Madura College, Madurai -625 011, Tamilnadu, India

² Department of Mathematics, The American College, Madurai - 625 002, Tamilnadu,India

Abstract

An H-magic labeling in a H-decomposable graph G is a bijection f : V (G) ∪ E(G) → {1, 2, ..., p + q} such that for every copy H in the decomposition, Σ_νεV(H) f(v) +  Σ_eεE(H) f(e) is constant. f is said to be H-E-super magic if f(E(G)) = {1, 2, · · · , q}. A family of subgraphs H₁,H₂, · · · ,H_h of G is a mixed cycle-decomposition of G if every subgraph H_i is isomorphic to some cycle C_k, for k ≥ 3, E(H_i) ∩ E(H_j) = ∅ for i ≠ j and ∪^h_i=1E(H_i) = E(G). In this paper, we prove that K_2m,2n is mixed cycle-E-super magic decomposable where m ≥ 2, n ≥ 3, with the help of the results found in [1].

Keywords

• H-decomposable graph
• H-E-super magic labeling
• mixed cycle-E-super magic decomposable graph