Some results on the independence number of connected domination critical graphs

AKCE International Journal of Graphs and Combinatorics

卷:15

T. Jiarasuksakun¹ 

[1] Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi126 Pracha Uthit Road, Bang Mod;

关键词: domination;    connected domination;    -critical graphs;    clique number;    independence number;   

DOI  :  10.1016/j.akcej.2017.09.004

来源: DOAJ

【 摘 要 】

A --critical graph is a graph with connected domination number and for any pair of non-adjacent vertices and of . Let and be respectively the clique number and the independence number of a graph. In this paper, we prove that every --critical graph satisfies for . We also characterize all --critical graphs achieving the upper bound. For , we show that there are infinitely many --critical graphs satisfying . Thus, we conclude this paper with an open problem that every --critical graph for satisfies .

【 授权许可】

Unknown