A Conjecture on Super Edge-Magic Total Labeling of 4-Cycle Books

Abstract

A graph G is called cycle books B 4 , m , 2 if G consists of m cycles C 4 with a common path P 2 . Figueroa-Centeno, Ichishima, and Muntaner-Batle conjecture that the graph B 4 , m , 2 is super edge-magic total if and only if m is even or m ≡ 5   mod 8 . In this article, we prove this conjecture for m ≥ 36 and m = 0 mod (2).