Classification of Efficient Dominating Sets of Circulant Graphs of Degree 5

被引：3

作者：

Kwon, Young Soo ^{[1
]}

Lee, Jaeun ^{[1
]}

Sohn, Moo Young ^{[2
]}

机构：

[1] Yeungnam Univ, Math, Kyongsan 712749, South Korea

[2] Changwon Natl Univ, Math, Chang Won 641773, South Korea

来源：

GRAPHS AND COMBINATORICS | 2022年 / 38卷 / 04期

基金：

新加坡国家研究基金会;

关键词：

Efficient dominating sets; Circulant graphs; PERFECT CODES;

D O I：

10.1007/s00373-022-02527-6

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

For a graph G, a subset D of V(G) is called an efficient dominating set of G if D is an independent set and every vertex in V(G) \ D is adjacent to exactly one vertex in the set D. In this paper, we give necessary and sufficient conditions for the existence of efficient dominating sets of circulant graphs of degree 5 and classify these sets.

引用

页数：8

共 50 条

[31] EQUIVALENCE DOMINATING SETS IN GRAPHS
Arumugam, S.
Sundarakannan, M.
UTILITAS MATHEMATICA, 2013, 91 : 231 - 242
[32] The Extended Dominating Sets in Graphs
Gao, Zhipeng
Shi, Yongtang
Xi, Changqing
Yue, Jun
ASIA-PACIFIC JOURNAL OF OPERATIONAL RESEARCH, 2023, 40 (05)
[33] Super Dominating Sets in Graphs
Lemanska, M.
Swaminathan, V.
Venkatakrishnan, Y. B.
Zuazua, R.
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES INDIA SECTION A-PHYSICAL SCIENCES, 2015, 85 (03) : 353 - 357
[34] DOMINATING SETS AND EIGENVALUES OF GRAPHS
ROWLINSON, P
BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 1994, 26 : 248 - 254
[35] Dominating sets in directed graphs
Pang, Chaoyi
Zhang, Rui
Zhang, Qing
Wang, Junhu
INFORMATION SCIENCES, 2010, 180 (19) : 3647 - 3652
[36] DOMINATING SETS IN PERFECT GRAPHS
CORNEIL, DG
STEWART, LK
DISCRETE MATHEMATICS, 1990, 86 (1-3) : 145 - 164
[37] Eternal dominating sets in graphs
School of Computing, University of North Florida, Jacksonville, FL 32224-2669, United States
不详
J. Comb. Math. Comb. Comp., 2009, (97-111): : 97 - 111
[38] Dominating sets in web graphs
Cooper, C
Klasing, R
Zito, M
ALGORITHMS AND MODELS FOR THE WEB-GRAPHS, PROCEEDINGS, 2004, 3243 : 31 - 43
[39] DOMINATING SETS IN CHORDAL GRAPHS
BOOTH, KS
JOHNSON, JH
SIAM JOURNAL ON COMPUTING, 1982, 11 (01) : 191 - 199
[40] Dominating sets in planar graphs
Matheson, LR
Tarjan, RE
EUROPEAN JOURNAL OF COMBINATORICS, 1996, 17 (06) : 565 - 568

← 1 2 3 4 5 →