# International Conference on Graph Theory and Combinatorics

May 16 – 18, 2014
Rogla, Slovenia
UTC timezone

## Vertex-transitive CIS graphs

Not scheduled
Rogla, Slovenia

### 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)

### Presentation materials

There are no materials yet.