### Speaker

Dr
Ademir Hujdurovic
(University of Primorska)

### Description

A {\it CIS} graph is a graph in which every maximal stable set and every maximal clique intersect.
A {\em well-covered} graph is a graph in which
all maximal stable sets are of the same size,
and {\em co-well-covered} if its complement is well-covered.
A {\it circulant} is a Cayley graph of a cyclic group.
A graph is said to be {\it vertex-transitive} if for every two vertices $u$ and $v$, there exists
an automorphism of the graph mapping $u$ to $v$.
Recently, Boros et al.~[Discrete Math.~318 (2014) 78--95] showed that a circulant is a CIS graph if and only if
it is well-covered, co-well-covered, and the product of its
clique and stability numbers equals to the number of vertices.
In this talk I will present the extension of this result to vertex-transitive graphs. I will also present the classification of of vertex-transitive CIS graphs with clique number at most $3$, and classification of vertex-transitive CIS graphs of valency at most 7.
Joint work with Edward Dobson, Martin Milani\v c and Gabriel Verret.

### Primary author

Dr
Ademir Hujdurovic
(University of Primorska)