Regular sets in circulant graphs with degree 3

被引：0
|
作者：
Hao, Yu-Xia [1 ]
Wang, Xiaomeng [2 ]
机构：
[1] Northwest Normal Univ, Coll Math & Stat, Lanzhou 730070, Gansu, Peoples R China
[2] Lanzhou Univ, Sch Math & Stat, Lanzhou 730000, Gansu, Peoples R China
来源：
DISCRETE APPLIED MATHEMATICS | 2024年 / 357卷
关键词：
Regular set; Circulant graph; Perfect code; Total perfect code; EFFICIENT DOMINATING SETS; PERFECT CODES;
D O I：
10.1016/j.dam.2024.05.033
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Let Gamma = (V, E) be a graph and a, b nonnegative integers. An (a, b)-regular set in Gamma is a nonempty proper subset D of V such that every vertex in D has exactly a neighbours in D and every vertex in V \ D has exactly b neighbours in D. In this paper, we obtain a necessary and sufficient condition for the existence of (a, b)-regular sets in connected circulant graphs with degree 3, for all possible values a, b. (c) 2024 Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.
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收藏
页码：51 / 55
页数：5
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