γ-Independent dominating graphs of paths and cycles

被引：0
|
作者：
Samanmoo, Roongrat [1 ]
Trakultraipruk, Nantapath [1 ]
Ananchuen, Nawarat [2 ]
机构：
[1] Thammasat Univ, Fac Sci & Technol, Dept Math & Stat, Pathum Thani 12120, Thailand
[2] Silpakorn Univ, Fac Sci, Dept Math, Nakhon Pathom 73000, Thailand
来源：
MAEJO INTERNATIONAL JOURNAL OF SCIENCE AND TECHNOLOGY | 2019年 / 13卷 / 03期
关键词：
independent dominating graph; independent dominating set; independent domination number;
D O I：
暂无
中图分类号：
O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];
学科分类号：
07 ; 0710 ; 09 ;
摘要：
An independent dominating set D of a graph G = (V(G),E( G)) is a set of pairwise non-adjacent vertices of G such that every vertex of G not in D is adjacent to at least one vertex in D. The independent domination number of G, denoted by gamma(i)(G), is the minimum cardinality of an independent dominating set of G. An independent dominating set of cardinality gamma(i)(G) is called a gamma(i)(G)-set. We introduce the gamma-independent dominating graph of G, denoted by ID gamma(G), as the graph whose vertex set is the set of all gamma(i)(G)-sets, and two gamma(i)(G)-sets are adjacent in ID gamma(G) if they differ by one vertex. In this paper we present the gamma-independent dominating graphs of all paths and all cycles.
引用
收藏
页码：245 / 256
页数：12
相关论文
共 50 条
  • [1] γ-total dominating graphs of paths and cycles
    Wongsriya, Alongkot
    Trakultraipruk, Nantapath
    [J]. SCIENCEASIA, 2017, 43 (05): : 326 - 333
  • [2] Hamilton Paths in Dominating Graphs of Trees and Cycles
    Kira Adaricheva
    Heather Smith Blake
    Chassidy Bozeman
    Nancy E. Clarke
    Ruth Haas
    Margaret-Ellen Messinger
    Karen Seyffarth
    [J]. Graphs and Combinatorics, 2022, 38
  • [3] 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)
  • [4] γ-induced-paired dominating graphs of paths and cycles
    Sanguanpong, Saharath
    Trakultraipruk, Nantapath
    [J]. DISCRETE MATHEMATICS ALGORITHMS AND APPLICATIONS, 2022, 14 (08)
  • [5] 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
  • [6] F-Paired Dominating Graphs of Some Paths and Some Cycles
    Eakawinrujee, Pannawat
    Trakultraipruk, Nantapath
    [J]. THAI JOURNAL OF MATHEMATICS, 2023, : 1 - 11
  • [7] On paths and cycles dominating hypercubes
    Dvorák, T
    Havel, I
    Mollard, M
    [J]. DISCRETE MATHEMATICS, 2003, 262 (1-3) : 121 - 129
  • [8] EXISTENCE OF DOMINATING CYCLES AND PATHS
    VELDMAN, HJ
    [J]. DISCRETE MATHEMATICS, 1983, 43 (2-3) : 281 - 296
  • [9] γ-Paired Dominating Graphs of Paths
    Eakawinrujee, Pannawat
    Trakultraipruk, Nantapath
    [J]. INTERNATIONAL JOURNAL OF MATHEMATICS AND COMPUTER SCIENCE, 2022, 17 (02): : 739 - 752
  • [10] DOMINATING CYCLES IN HALIN GRAPHS
    SKOWRONSKA, M
    SYSLO, MM
    [J]. DISCRETE MATHEMATICS, 1990, 86 (1-3) : 215 - 224
12345