Abstract

Let G be a graph with vertex set V = V (G) and edge set E = E(G) and let m = jE(G)j and n = jV (G)j. A one-to-one map f from V [ E onto the integers f1; 2; 3; :::;m + ng is called vertex magic total labeling if there is a constant k so that for every vertex u, f(u) + P f(uv) = k where the sum is over all vertices v adjacent to u. Let us call the sum of labels at vertex u the weight wf (u) of the vertex under labeling f; we require wf (u) = k for all u. The constant k is called the magic constant for f. Such a labeling is odd if f(V (G)) = f1; 3; 5; :::; 2n

Keywords

References

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