Perfect Isolate Domination in Graphs

被引：2
|
作者：
Armada, Cris L. [1 ,3 ]
Hamja, Jamil J. [2 ]
机构：
[1] Cebu Normal Univ, Coll Arts & Sci, Math Dept, Cebu, Philippines
[2] MSU Tawi Tawi Coll Technol & Oceanog, Off Vice Chancellor Acad Affairs, Tawi Tawi 7500, Philippines
[3] Cebu Normal Univ, Ctr Res & Dev, Cebu, Philippines
来源：
EUROPEAN JOURNAL OF PURE AND APPLIED MATHEMATICS | 2023年 / 16卷 / 02期
关键词：
Perfect domination; isolate domination; perfect isolate domination;
D O I：
10.29020/nybg.ejpam.v16i2.4760
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Let G = (V (G), E(G)) be a simple connected graph. A set S subset of V (G) is said to be a perfect isolate dominating set of G if S is a perfect dominating set and an isolate dominating set of G. The minimum cardinality of a perfect isolate dominating set of G is called perfect isolate domination number, and is denoted by gamma p0(G). A perfect isolate dominating set S with |S| = gamma p0(G) is said to be gamma p0-set. In this paper, the author gives a characterization of perfect isolate dominating set of some graphs and graphs obtained from the join, corona and lexicographic product of two graphs. Moreover, the perfect isolate domination number of the forenamed graphs is determined and also, graphs having no perfect isolate dominating set are examined.
引用
收藏
页码：1326 / 1341
页数：16
相关论文
共 50 条
  • [31] Perfect Equitable Isolate Dominations in Graphs
    Caay, Mark L.
    Hernandez, Andrew C.
    EUROPEAN JOURNAL OF PURE AND APPLIED MATHEMATICS, 2024, 17 (02): : 969 - 978
  • [32] Perfect Matchings in Total Domination Critical Graphs
    Michael A. Henning
    Anders Yeo
    Graphs and Combinatorics, 2011, 27 : 685 - 701
  • [33] Upper domination and upper irredundance perfect graphs
    Gutin, G
    Zverovich, VE
    DISCRETE MATHEMATICS, 1998, 190 (1-3) : 95 - 105
  • [34] Perfect Italian domination on planar and regular graphs
    Lauri, Juho
    Mitillos, Christodoulos
    DISCRETE APPLIED MATHEMATICS, 2020, 285 : 676 - 687
  • [35] Extremal perfect graphs for a bound on the domination number
    Blidia, Mostafa
    Chellali, Mustapha
    Maffray, Frederic
    DISCRETE MATHEMATICS, 2008, 308 (10) : 1785 - 1791
  • [36] Independent perfect domination sets in Cayley graphs
    Lee, J
    JOURNAL OF GRAPH THEORY, 2001, 37 (04) : 213 - 219
  • [37] Perfect graphs involving semitotal and semipaired domination
    Haynes, Teresa W.
    Henning, Michael A.
    JOURNAL OF COMBINATORIAL OPTIMIZATION, 2018, 36 (02) : 416 - 433
  • [38] Complexity issues of perfect secure domination in graphs
    Chakradhar, P.
    Reddy, P. Venkata Subba
    RAIRO-THEORETICAL INFORMATICS AND APPLICATIONS, 2021, 55
  • [39] Complexity Issues of Perfect Roman Domination in Graphs
    Chakradhar, Padamutham
    Reddy, Palagiri Venkata Subba
    KYUNGPOOK MATHEMATICAL JOURNAL, 2021, 61 (03): : 661 - 669
  • [40] Perfect graphs involving semitotal and semipaired domination
    Teresa W. Haynes
    Michael A. Henning
    Journal of Combinatorial Optimization, 2018, 36 : 416 - 433
12345