A note on the domination dot-critical graphs

Xue gang Chen*, Wai Chee Shiu

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

4 Citations (Scopus)


A graph G is dot-critical if contracting any edge decreases the domination number. Nader Jafari Rad (2009) [3] posed the problem: Is it true that a connected k-dot-critical graph G with G = 0{combining long solidus overlay} is 2-connected? In this note, we give a family of 1-connected 2 k-dot-critical graph with G = 0{combining long solidus overlay} and show that this problem has a negative answer.

Original languageEnglish
Pages (from-to)3743-3745
Number of pages3
JournalDiscrete Applied Mathematics
Issue number18
Publication statusPublished - 28 Nov 2009

Scopus Subject Areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

User-Defined Keywords

  • Complete bipartite graph
  • Domination dot-critical
  • Domination number


Dive into the research topics of 'A note on the domination dot-critical graphs'. Together they form a unique fingerprint.

Cite this