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## Discussiones Mathematicae Graph Theory

2014 | 34 | 4 | 683-690
Tytuł artykułu

### The Connectivity Of Domination Dot-Critical Graphs With No Critical Vertices

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
An edge of a graph is called dot-critical if its contraction decreases the domination number. A graph is said to be dot-critical if all of its edges are dot-critical. A vertex of a graph is called critical if its deletion decreases the domination number. In A note on the domination dot-critical graphs, Discrete Appl. Math. 157 (2009) 3743-3745, Chen and Shiu constructed for each even integer k ≥ 4 infinitely many k-dot-critical graphs G with no critical vertices and k(G) = 1. In this paper, we refine their result and construct for integers k ≥ 4 and l ≥ 1 infinitely many k-dot-critical graphs G with no critical vertices, k(G) = 1 and λ(G) = l. Furthermore, we prove that every 3-dot- critical graph with no critical vertices is 3-connected, and it is best possible.
Słowa kluczowe
EN
Wydawca
Czasopismo
Rocznik
Tom
Numer
Strony
683-690
Opis fizyczny
Daty
wydano
2014-11-01
otrzymano
2013-07-08
poprawiono
2013-09-20
zaakceptowano
2013-09-30
online
2014-11-15
Twórcy
autor
• Department of Mathematical Information Science, Tokyo University of Science, 1-3 Kagurazaka, Shinjuku-ku, Tokyo, michitaka.furuya@gmail.com
Bibliografia
• [1] T. Burton and D.P. Sumner, Domination dot-critical graphs, Discrete Math. 306 (2006) 11-18. doi:10.1016/j.disc.2005.06.029
• [2] X. Chen and W.C. Shiu, A note on the domination dot-critical graphs, Discrete Appl. Math. 157 (2009) 3743-3745. doi:10.1016/j.dam.2009.07.014
• [3] R. Diestel, Graph Theory 4th Edition (Verlag, Heidelberg, Springer, 2010).
• [4] M. Furuya and M. Takatou, Upper bound on the diameter of a domination dot- critical graph, Graphs Combin. 29 (2013) 79-85. doi:10.1007/s00373-011-1095-1
• [5] D.A. Mojdeh and S. Mirzamani, On the diameter of dot-critical graphs, Opuscula Math. 29 (2009) 165-175.
• [6] N.J. Rad, On the diameter of a domination dot-critical graph, Discrete Appl. Math. 157 (2009) 1647-1649. doi:10.1016/j.dam.2008.10.015
Typ dokumentu
Bibliografia
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