The Petersen graph has no quantum symmetry

Errantum: Petersen graph has branchwidth 4

In my doctoral thesis [1], I claimed a proof that the branchwidth of the Petersen graph had branchwidth 5 and proceeded to prove that it was a member of the obstruction set for graphs with branchwidth at most 4. I have stated this claim in Hicks [2] and Hicks et al. [4]. There was, however, an error in the construction of the tangle used to prove the claim. The branchwidth of the Petersen graph...

Addressing the Petersen graph

Motivated by a problem on message routing in communication networks, Graham and Pollak proposed a scheme for addressing the vertices of a graph G by N -tuples of three symbols in such a way that distances between vertices may readily be determined from their addresses. They observed that N ≥ h(D), the maximum of the number of positive and the number of negative eigenvalues of the distance matri...

The ubiquitous Petersen graph

Chartrand, G., H. Hevia and R.J. Wilson, The ubiquitous Petersen graph, Discrete Mathematics 100 (1992) 303-311.

On the Relation between the Petersen Graph

Extending the dual of the Petersen graph

By hypotheses (a) and (c), if {i, j} is a 2-element subset of the type set I of Γ, then there are flags F of co-type {i, j}, such that res(F ) is a rank 2 geometry over the type set {i, j}, and all such {i, j}-residues are isomorphic. Hence, such a geometry Γ can be described by a diagram, in which the types (or even the exact isomorphism types) of all rank-2-residues are listed; this is often ...