SEMITOTAL DOMINATION IN CLAW-FREE GRAPHS

被引：0

作者：

Chen, Jie ^{[1
]}

Liang, Yi-Ping ^{[1
]}

Xu, Shou-Jun ^{[1
]}

机构：

[1] Lanzhou Univ, Gansu Ctr Appl Math, Sch Math & Stat, Lanzhou 730000, Gansu, Peoples R China

来源：

DISCUSSIONES MATHEMATICAE GRAPH THEORY | 2024年 / 44卷 / 04期

基金：

中国国家自然科学基金;

关键词：

semitotal domination; minimum degree; claw-free graphs;

D O I：

10.7151/dmgt.2512

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In an isolate-free graph G, a subset S of vertices is a semitotal dominating set of G if it is a dominating set of G and every vertex in S is within distance 2 of another vertex of S. The semitotal domination number of G, denoted by 7t2(G), is the minimum cardinality of a semitotal dominating set in G. We prove that if G is a connected claw-free graph of order n with minimum degree delta(G) ,, 2 and is not one of fourteen exceptional graphs (ten of which are cycles), then 7t2(G) 5 37 n, and we also characterize the graphs achieving equality, which are an infinite family of graphs. In particular, if we restrict (2014) 67-81].

引用

页码：1585 / 1605

页数：21

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