PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
2003 | 23 | 1 | 159-162
Tytuł artykułu

Perfect connected-dominant graphs

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
If D is a dominating set and the induced subgraph G(D) is connected, then D is a connected dominating set. The minimum size of a connected dominating set in G is called connected domination number $γ_c(G)$ of G. A graph G is called a perfect connected-dominant graph if $γ(H) = γ_c(H)$ for each connected induced subgraph H of G.We prove that a graph is a perfect connected-dominant graph if and only if it contains no induced path P₅ and induced cycle C₅.
Wydawca
Rocznik
Tom
23
Numer
1
Strony
159-162
Opis fizyczny
Daty
wydano
2003
otrzymano
2001-08-16
Twórcy
  • RUTCOR, Rutgers University, 640 Bartholomew Rd., Piscataway, NJ 08854 USA
Bibliografia
  • [1] S. Arumugam and J.J. Paulraj, On graphs with equal domination and connected domination numbers, Discrete Math. 206 (1999) 45-49, doi: 10.1016/S0012-365X(98)00390-2.
  • [2] K. Arvind and R.C. Pandu, Connected domination and Steiner set on weighted permutation graphs, Inform. Process. Lett. 41 (1992) 215-220, doi: 10.1016/0020-0190(92)90183-V.
  • [3] H. Balakrishnan, A. Rajaram and R.C. Pandu, Connected domination and Steiner set on asteroidal triple-free graphs, Lecture Notes Math. 709 (1993) 131-141.
  • [4] C. Bo and B. Liu, Some inequalities about connected domination number, Discrete Math. 159 (1996) 241-245, doi: 10.1016/0012-365X(95)00088-E.
  • [5] J.E. Dunbar, J.W. Grossman, J.H. Hattingh, S.T. Hedetniemi and A.A. McRae, On weakly connected domination in graphs, Discrete Math. 167/168 (1997) 261-269, doi: 10.1016/S0012-365X(96)00233-6.
  • [6] D.V. Korobitsyn, On the complexity of determining the domination number in monogenic classes of graphs, Discrete Math. 2 (1990) 90-96.
  • [7] J.J. Paulrau and S. Arumugam, On connected cutfree domination in graphs, Indian J. Pure Appl. Math. 23 (1992) 643-647.
  • [8] L. Sun, Some results on connected domination of graphs, Math. Appl. 5 (1992) 29-34.
  • [9] E.S. Wolk, A note on 'The comparability graph of a tree', Proc. Amer. Math. Soc. 16 (1966) 17-20, doi: 10.1090/S0002-9939-1965-0172274-5.
  • [10] E.S. Wolk, The comparability graph of a tree, Proc. Amer. Math. Soc. 13 (1962) 789-795.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1192
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.