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

Mudin Simanihuruk, Tri Atmojo Kusmayadi, Baki Swita, Minsi Romala and Friska Damanik

International Journal of Mathematics and Mathematical Sciences, 2021, vol. 2021, issue 1

Abstract: A graph G is called cycle books B[(4, m), 2] if G consists of m cycles C4 with a common path P2. 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).

Date: 2021
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https://doi.org/10.1155/2021/8483926

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