Labeling of 2-regular Graphs by Odd Edge Magic

Abstract

An edge magic total labeling of a graph G(p, q) is said to be an Odd edge magic total labeling if λ(E) = {1,3, …2q – 1} with the condition that for each edge uv ∈ E, λ(u) + λ(uv) +λ(v) = ke, where ke is known as the magic constant. In this paper we resolute cycles of odd length, disjoint union of C3 ∪ C4r+2 (r ≥ 1), disjoint union of C4 ∪ C4r-1 (r > 1), disjoint union of C3 ∪ C4r (r > 1), disjoint union of C4 ∪ C4r-3 (r > 1), are Odd edge magic graphs.