Disprove of a Conjecture on the Doubly Connected Domination Subdivision Number

被引：1

作者：

Kosari, Saeed ^{[1
]}

Shao, Zehui ^{[1
]}

Sheikholeslami, Seyed Mahmoud ^{[2
]}

Karami, Hossein ^{[2
]}

Volkmann, Lutz ^{[3
]}

机构：

[1] Guangzhou Univ, Inst Comp Sci & Technol, Guangzhou 510006, Peoples R China

[2] Azarbaijan Shahid Madani Univ, Dept Math, Tabriz, Iran

[3] Rhein Westfal TH Aachen, Lehrstuhl Math 2, D-52056 Aachen, Germany

来源：

BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY | 2022年 / 48卷 / 04期

基金：

中国国家自然科学基金; 国家重点研发计划;

关键词：

Doubly connected domination number; Doubly connected domination subdivision number;

D O I：

10.1007/s41980-021-00586-8

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A set S of vertices of a connected graph G is a doubly connected dominating set (DCDS) if every vertex not in S is adjacent to some vertex in S and the subgraphs induced by S and V - S are connected. The doubly connected domination number gamma(cc)(G) is the minimum size of such a set. The doubly connected domination subdivision number sd(gamma cc) (G) is the minimum number of edges that must be subdivided (each edge in G can be subdivided at most once) to increase the doubly connected domination number. It was conjectured (Karami et al. in Mat Vesnic 64:232-239, 2012) that the doubly connected domination subdivision number of a connected planar graph is at most two. In this paper, we disprove this conjecture by showing that the doubly connected domination subdivision number of the regular icosahedron graph is three.

引用

页码：1351 / 1355

页数：5

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