Some Edge-magic Cubic Graphs:

W. C. Shiut1, Sin-Min Lee 2
1Department of Mathematics Hong Kong Baptist University 224 Waterloo Road, Kowloon Tong Hong Kong, China.
2 Department of Mathematics and Computer Science San José State University One Washington Square, San José, CA 95192-0103, U.S.A.

Abstract

It was conjectured by Lee that a cubic simple graph with \(4k + 2\) vertices is edge-magic [5]. In this paper we show that the conjecture is not true for multigraphs or disconnected simple graphs in general. Several new classes of cubic edge-magic graphs are exhibited.