The exact 2-domination number of generalized Petersen graphs

被引：0

作者：

Chen, Xue-gang ^{[1
]}

Zhao, Xue-song ^{[1
]}

机构：

[1] North China Elect Power Univ, Dept Math, Beijing 102206, Peoples R China

来源：

PROCEEDINGS OF THE INDIAN ACADEMY OF SCIENCES-MATHEMATICAL SCIENCES | 2020年 / 130卷 / 01期

关键词：

2-Domination number; generalized Petersen graph;

D O I：

10.1007/s12044-020-00571-x

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let G = (V, E) be a graph. A subset S subset of V is a 2-dominating set of G if each vertex in V - S is adjacent to at least two vertices in S. The 2-domination number of G is the cardinality of the smallest 2-dominating set of G. In this paper, we shall prove that the 2-domination number of generalized Petersen graphs P(5k+ 1, 3), P(5k+ 2, 3) and P(5k + 3, 3) is 4k + 2, 4k + 3 and 4k + 4, respectively. This proves one conjecture due to Bakhshesh et al.

引用

页数：6

共 5 条

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Fink J.F., 1985, Graph Theory with Applications to Algorithms and Computer Science, P282

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Li ZX, 2013, 2013 SIXTH INTERNATIONAL CONFERENCE ON ADVANCED COMPUTATIONAL INTELLIGENCE (ICACI), P12, DOI 10.1109/ICACI.2013.6748466

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