(Strong) Proper vertex connection of some digraphs

被引：1
|
作者：
Nie, Kairui [1 ]
Ma, Yingbin [1 ]
Sidorowicz, Ezbieta [2 ]
机构：
[1] Henan Normal Univ, Coll Math & Informat Sci, Xinxiang 453007, Peoples R China
[2] Univ Zielona Gora, Inst Math, Zielona Gora, Poland
来源：
APPLIED MATHEMATICS AND COMPUTATION | 2023年 / 458卷
基金：
中国国家自然科学基金; 中国博士后科学基金;
关键词：
Properly vertex connected; Strong properly vertex connected; Digraph; Vertex-coloring; RAINBOW CONNECTION; NUMBER;
D O I：
10.1016/j.amc.2023.128243
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The (strong) proper vertex connection number ⃖⃖⃖⃖⃖⃖⃗⃖������������������������(& UGamma;), (������)������������������-number for short, is denoted as the smallest cardinality of colors required to color the digraph & UGamma; so that & UGamma; is (strong) properly vertex connected. The ������������������-number and the ������������������������-number are calculated for some unique classes of digraphs in this paper, along with some fundamental results on these parameters. It is known that the ������������������-number is not exceeding 3 for any strong digraph. For digraphs with ������������������-number not exceeding 2, we provide some sufficient conditions. Furthermore, we prove that the ������������������������-number is at most 3 for any minimal strongly connected digraph, but it can be arbitrarily large for some strong digraphs.
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