Cycle-based super edge-magic graphs and their super edge-magic sequences (Q2224038)

Summary: In this paper, we have introduced a new concept of super edge-magic sequence (SEMS) of a super edge-magic graph (SEMG) with \(p\) vertices and \(q\) edges. The super edge-magic sequence of natural numbers is denoted by \(x_{i}\), \(1 \leq i \leq q\). This sequence need not to be monotonic. We also extend the notion of cycle iteratively for constructing new SEMS based on the `sequence for cycle', from which we acquire some families like Petersen graph and its extension, web graph and its extension and others.