Hamilton Paths in Dominating Graphs of Trees and Cycles

被引：0

作者：

Kira Adaricheva

Heather Smith Blake

Chassidy Bozeman

Nancy E. Clarke

Ruth Haas

Margaret-Ellen Messinger

Karen Seyffarth

机构：

[1] Hofstra University,Department of Mathematics

[2] Davidson College,Department of Mathematics and Computer Science

[3] Mount Holyoke College,Department of Mathematics and Statistics

[4] Acadia University,Department of Mathematics and Statistics

[5] University of Hawaii at Mānoa,Department of Mathematics

[6] Mount Allison University,Department of Mathematics and Computer Science

[7] University of Calgary,Department of Mathematics and Statistics

来源：

Graphs and Combinatorics | 2022年 / 38卷

关键词：

Reconfiguration; Domination; Hamilton paths;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

The dominating graph of a graph H has as its vertices all dominating sets of H, with an edge between two dominating sets if one can be obtained from the other by the addition or deletion of a single vertex of H. In this paper we prove that the dominating graph of any tree has a Hamilton path. We also show how a result about binary strings leads to a proof that the dominating graph of a cycle on n vertices has a Hamilton path if and only if n is not a multiple of 4.

引用

共 50 条

[1] Hamilton Paths in Dominating Graphs of Trees and Cycles
Adaricheva, Kira
Blake, Heather Smith
Bozeman, Chassidy
Clarke, Nancy E.
Haas, Ruth
Messinger, Margaret-Ellen
Seyffarth, Karen
[J]. GRAPHS AND COMBINATORICS, 2022, 38 (06)
[2] γ-total dominating graphs of paths and cycles
Wongsriya, Alongkot
Trakultraipruk, Nantapath
[J]. SCIENCEASIA, 2017, 43 (05): : 326 - 333
[3] γ-Independent dominating graphs of paths and cycles
Samanmoo, Roongrat
Trakultraipruk, Nantapath
Ananchuen, Nawarat
[J]. MAEJO INTERNATIONAL JOURNAL OF SCIENCE AND TECHNOLOGY, 2019, 13 (03) : 245 - 256
[4] HAMILTON CYCLES AND PATHS IN BUTTERFLY GRAPHS
WONG, SA
[J]. NETWORKS, 1995, 26 (03) : 145 - 150
[5] γ-induced-paired dominating graphs of paths and cycles
Sanguanpong, Saharath
Trakultraipruk, Nantapath
[J]. DISCRETE MATHEMATICS ALGORITHMS AND APPLICATIONS, 2022, 14 (08)
[6] Coalition Graphs of Paths, Cycles, and Trees
Haynes, Teresa
Hedetniemi, Jason
Hedetniemi, Stephen T.
McRae, Alice
Mohan, Raghuveer
[J]. DISCUSSIONES MATHEMATICAE GRAPH THEORY, 2023, 43 (04) : 931 - 946
[7] Approximately counting Hamilton paths and cycles in dense graphs
Dyer, M
Frieze, A
Jerrum, M
[J]. SIAM JOURNAL ON COMPUTING, 1998, 27 (05) : 1262 - 1272
[8] AN ALGORITHM FOR FINDING HAMILTON PATHS AND CYCLES IN RANDOM GRAPHS
BOLLOBAS, B
FENNER, TI
FRIEZE, AM
[J]. COMBINATORICA, 1987, 7 (04) : 327 - 341
[9] LONG DOMINATING CYCLES AND PATHS IN GRAPHS WITH LARGE NEIGHBORHOOD UNIONS
BROERSMA, HJ
VELDMAN, HJ
[J]. JOURNAL OF GRAPH THEORY, 1991, 15 (01) : 29 - 38
[10] F-Paired Dominating Graphs of Some Paths and Some Cycles
Eakawinrujee, Pannawat
Trakultraipruk, Nantapath
[J]. THAI JOURNAL OF MATHEMATICS, 2023, : 1 - 11

← 1 2 3 4 5 →