Outer-connected domination in 2-connected cubic graphs

被引：1
|
作者：
Wang, Shipeng [1 ]
Wu, Baoyindureng [1 ]
An, Xinhui [1 ]
Liu, Xiaoping [2 ]
Deng, Xingchao [3 ]
机构：
[1] Xinjiang Univ, Coll Math & Syst Sci, Urumqi 830046, Xinjiang, Peoples R China
[2] Xinjiang Inst Engn, Fdn Dept, Urumqi 830000, Xinjiang, Peoples R China
[3] LPMC TJKLC Nankai Univ, Ctr Combinator, Tianjin 300071, Peoples R China
来源：
DISCRETE MATHEMATICS ALGORITHMS AND APPLICATIONS | 2014年 / 6卷 / 03期
关键词：
Domination number; outer-connected domination number; cubic graphs;
D O I：
10.1142/S1793830914500323
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
A set S of vertices of a graph G is an outer-connected dominating set if every vertex not in S is adjacent to some vertex in S and the subgraph induced by V\S is connected. The outer-connected domination number gamma(c)(G) is the minimum size of such a set. We present an infinite family of 2-connected cubic graphs, in which the number of vertices in a longest path are much less than the half of their orders. This disprove a recent conjecture posed by Akhbari, Hasni, Favaron, Karami, Sheikholeslami.
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页数：5
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