期刊论文

Wang, Chunxiang

英文

Graphs and Combinatorics

0911-0119

2016

32

1

377-402

10.1007/s00373-015-1554-1

The authors would like to express their sincere gratitude to the referees for a very careful reading of the paper and for all of their insightful comments and valuable suggestions, which led to a number of improvements in this paper. This work was supported by the National Natural Science Foundation of China (Grant No. 11271149 and 11371162). Financially supported by self-determined research funds of CCNU from the colleges basic research and operation of MOE.

本校为第一且通讯机构

A set of vertices in graph is a total dominating set of if every vertex of is adjacent to some vertex in . The minimum cardinality of a total dominating set of is the total domination number . A graph with no isolated vertex is total domination vertex critical if for any vertex of that is not adjacent to a vertex of degree one, the total domination number of is less than the total domination number of . We call such graphs -critical. If such a graph has total domination number , we call it --critical. It is well known from Sohn et al. (Discrete Appl Math 159:46-52, 2011) that the only remainin...