Abstract
A graph G is called (a, b)-cycle books B[(Ca, m), (Cb, n), Pt] if G consists of m cycles Ca and n cycles Cb with a common path Pt. In this article we show that the (7, 3)-cycle books B[(C7, 1), (C3, n), P2] admits edge-magic total labeling. In addition we prove that (a, 3)-cycle books B[(Ca, 1), (C3, n), P2] admits super edge-magic total labeling for a = 7 and extends the values of a to 4x − 1 for any positive integer x. Moreover we prove that the (7, 3)-cycle books B[(C7, 2), (C3, n), P2] admits super edge-magic total labeling.
Highlights
Let G be a graph such that |V (G)| = p and |E(G)| = q
By Theorem 1 and Claim 1, we conclude that G is super edge-magic total
By Theorem 1 and Claim 1 of Lemma 6, we conclude that G is super edge-magic total with magic constant k = p+q+s = n+7+2n+7+5 = 3n + 19
Summary
We provide some previous results on super edge-magic total labeling of a graph. Super Edge Magic Total Labeling of (7,3)-Cycle Books.
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