On Super Edge-magic Total Labeling of Modified Watermill Graph

Abstract

An edge-magic total labeling on a graph G is one-to-one map from V ( G ) ∪ E ( G ) onto the set of integers 1,2, ..., ν + e , where ν = | V ( G )| and e = | E ( G )|, with the property that, given any edge uv , f ( u ) + f ( u , ν }) + f ( ν ) = k for every u , v ∈ V ( G ), and k is called magic valuation . An edge-magic total labeling f is called super edge-magic total if f ( v ( G )) = {1,2 ...,| V ( G )|} and f ( E ( G )) = {| V ( G )| + 1, | V ( G )| + 2,... | V ( G ) + E ( G )|}. In this paper we investigate edge-magic total labeling of a new graph called modified Watermill graph . Furthermore, the magic valuation of the modified Watermill graph WM ( n ) is , for n odd, n ≥ 3.

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