Λεπτομέρειες βιβλιογραφικής εγγραφής
| Τίτλος: |
Vertex‐Distinguishing and Sum‐Distinguishing Edge Coloring of Regular Graphs. |
| Συγγραφείς: |
Gao, Yuping1 (AUTHOR) gaoyp@lzu.edu.cn, Shan, Songling2 (AUTHOR), Wang, Guanghui3,4 (AUTHOR) |
| Πηγή: |
Journal of Graph Theory. Sep2026, Vol. 113 Issue 1, p73-87. 15p. |
| Θεματικοί όροι: |
*Regular graphs, *Graph coloring, *Graph theory |
| Περίληψη: |
Given an integer k≥1, an edge‐k‐coloring of a graph G is an assignment of k colors 1,...,k to the edges of G such that no two adjacent edges receive the same color. A vertex‐distinguishing (resp. sum‐distinguishing) edge‐k‐coloring of G is an edge‐k‐coloring such that for any two distinct vertices u and v, the set (resp. sum) of colors taken from all the edges incident with u is different from that taken from all the edges incident with v. The vertex‐distinguishing chromatic index (resp. sum‐distinguishing chromatic index), denoted χvd′(G) (resp. χsd′(G)), is the smallest value k such that G has a vertex‐distinguishing edge‐k‐coloring (resp. sum‐distinguishing edge‐k‐coloring). Let G be a d‐regular graph on n vertices, where n is even and sufficiently large. We show that χvd′(G)=d+2 if d is arbitrarily close to n/2 from above, and χsd′(G)=d+2 if d≥2n3. Our first result strengthens a result of Balister et al. for such class of regular graphs, and our second result constitutes a significant advancement in the field of sum‐distinguishing edge coloring. To achieve these results, we introduce novel edge coloring results which may be of independent interest. [ABSTRACT FROM AUTHOR] |
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