A note on the domination dot-critical graphs |
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| Authors: | Xue-gang Chen Wai Chee Shiu |
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| Institution: | a Department of Mathematics, North China Electric Power University, Beijing 102206, China
b Department of Mathematics, Hong Kong Baptist University, 224 Waterloo Road, Kowloon Tong, Hong Kong, China |
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| Abstract: | 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? is 2-connected? In this note, we give a family of 1-connected 2k-dot-critical graph with G′=0? and show that this problem has a negative answer. |
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| Keywords: | Domination dot-critical Domination number Complete bipartite graph |
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