Integral sum graphs Gn and G-r,n are perfect graphs
| Autor: | Julia K. Abraham, Sajidha P., Lowell W. Beineke, Vilfred V., L. Mary Florida |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2024 |
| Předmět: | |
| Zdroj: | AKCE International Journal of Graphs and Combinatorics, Vol 21, Iss 1, Pp 77-83 (2024) |
| Druh dokumentu: | article |
| ISSN: | 09728600 2543-3474 0972-8600 |
| DOI: | 10.1080/09728600.2023.2251046 |
| Popis: | AbstractA graph G is an integral sum graph (sum graph) if its vertices can be labeled with distinct integers (positive integers) so that e = uv is an edge of G if and only if the sum of the labels on vertices u and v is also a label in G. A graph G is perfect if the chromatic number of each of its induced subgraphs is equal to the clique number of the same. A simple graph G is of class 1 if its edge chromatic number and maximum degree are same. In this paper, we prove that integral sum graphs Gn, [Formula: see text] and [Formula: see text] over the label sets [Formula: see text] and [Formula: see text], respectively, are perfect graphs as well as of class 1 for [Formula: see text]. We also obtain a few structural properties of these graphs. |
| Databáze: | Directory of Open Access Journals |
| Externí odkaz: |
|