On $\alpha$-excellent graphs

M. Dettlaff; M. A. Henning; J. Topp

On $\alpha$-excellent graphs

Combinatorics 2022-08-19 v1

Authors: M. Dettlaff , M. A. Henning , J. Topp

Abstract

A graph $G$ is $\alpha$ -excellent if every vertex of $G$ is contained in some maximum independent set of $G$ . In this paper, we characterize $\alpha$ -excellent bipartite graphs, $\alpha$ -excellent unicyclic graphs, $\alpha$ -excellent simplicial graphs, $\alpha$ -excellent chordal graphs, $\alpha$ -excellent block graphs, and we show that every generalized Petersen graph is $\alpha$ -excellent.

Keywords

bipartite graphs graph theory of groups graph theory

Cite

@article{arxiv.2208.08498,
  title  = {On $\alpha$-excellent graphs},
  author = {M. Dettlaff and M. A. Henning and J. Topp},
  journal= {arXiv preprint arXiv:2208.08498},
  year   = {2022}
}

Comments

15 pages, 4 figures

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