Vertex-transitive CIS graphs
Abstract
A CIS graph is a graph in which every maximal stable set and every maximal clique intersect. A graph is well-covered if all its maximal stable sets are of the same size, co-well-covered if its complement is well-covered, and vertex-transitive if, for every pair of vertices, there exists an automorphism of the graph mapping one to the other. We show that a vertex-transitive graph is CIS if and only if it is well-covered, co-well-covered, and the product of its clique and stability numbers equals its order. A graph is irreducible if no two distinct vertices have the same neighborhood. We classify irreducible well-covered CIS graphs with clique number at most 3 and vertex-transitive CIS graphs of valency at most 7, which include an infinite family. We also exhibit an infinite family of vertex-transitive CIS graphs which are not Cayley.
Cite
@article{arxiv.1405.7874,
title = {Vertex-transitive CIS graphs},
author = {Edward Dobson and Ademir Hujdurović and Martin Milanič and Gabriel Verret},
journal= {arXiv preprint arXiv:1405.7874},
year = {2016}
}