Vertex-transitive expansions of (1, 3)-trees

Vertex-Transitive Polyhedra in 3-Space

In addition to regular and chiral polyhedra, which have been extensively studied, the vertextransitive polyhedra of higher genus also present an attractive and worthwhile challenge. While the definition is combinatorial, the problem at hand is the realization in Euclidean 3-space as a highly symmetric, non-self-intersecting polyhedron in the more classical sense (with flat, non-self-intersectin...

Vertex Equitable Labelings of Transformed Trees

Vertex-transitive CIS graphs

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 o...

3 1 Ja n 20 06 QUANTUM AUTOMORPHISM GROUPS OF VERTEX - TRANSITIVE GRAPHS OF ORDER ≤ 11

We study quantum automorphism groups of vertex-transitive graphs having less than 11 vertices. With one possible exception, these can be obtained from cyclic groups Zn, symmetric groups Sn and quantum symmetric groups Qn, by using various product operations. The exceptional case is that of the Petersen graph, and we present some questions about it.

Cores of Vertex Transitive Graphs

A core of a graph X is a vertex minimal subgraph to which X admits a homomorphism. Hahn and Tardif have shown that for vertex transitive graphs, the size of the core must divide the size of the graph. This motivates the following question: when can the vertex set of a vertex transitive graph be partitioned into sets each of which induce a copy of its core? We show that normal Cayley graphs and ...