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 |