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Domination dot-critical graphs with no critical vertices
Authors:Zhao Chengye  Sun Linlin
Institution:Department of Computer Science, Dalian University of Technology, Dalian, 116024, PR China
Abstract:A graph G is dot-critical if contracting any edge decreases the domination number. It is totally dot-critical if identifying any two vertices decreases the domination number. Burton and Sumner Discrete Math. 306 (2006) 11-18] posed the problem: Is it true that for k?4, there exists a totally k-dot-critical graph with no critical vertices? In this paper, we show that this problem has a positive answer.
Keywords:Domination  Dot-critical  Critical vertex
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