| 言語種別 | 英語 |
|---|---|
| 発行・発表の年月 | 2024 |
| 形態種別 | 学術雑誌 |
| 査読 | 査読あり |
| 標題 | Recent studies on the super edge-magic deficiency of graphs |
| 執筆形態 | 共著 |
| 掲載誌名 | Theory and Applications of Graphs |
| 掲載区分 | 国外 |
| 出版社・発行元 | Discrete Mathematics and Combinatorics Commons |
| 巻・号・頁 | 11(1),1-11 |
| 総ページ数 | 11 |
| 担当区分 | 筆頭著者 , 責任著者 |
| 国際共著 | 国際共著 |
| 著者・共著者 | Rikio Ichishima, Susana C. Lopez, Francesc Muntaner, Yukio Takahashi |
| 概要 | In this paper, we introduce the
parameter l(n) as the minimum size of a graph G of order n for which all graphs of order n and size at least l(n) have µs (G) = +∞, and provide lower and upper bounds for l(n). Imran, Baig, and Fe˘nov˘c´ıkov´a established that for integers n with n ≡ 0 (mod 4), µs (Dn) ≤ 3n/2 − 1, where Dn is the cartesian product of the cycle Cn of order n and the complete graph K2 of order 2. We improve this bound by showing that µs (Dn) ≤ n + 1 when n ≥ 4 is even. Enomoto, Llad´o, Nakamigawa, and Ringel posed the conjecture that every nontrivial tree is super edge-magic. We propose a new approach to attack this conjecture. This approach may also help to resolve another labeling conjecture on trees by Graham and Sloane. |
| researchmap用URL | https://digitalcommons.georgiasouthern.edu/tag/vol11/iss1/1 |