Non-isomorphic signatures on some generalised Petersen graph

Some topological properties of folded Petersen graph

The k-dimensional folded Petersen graph, FPk , is an iterative Cartesian product on the simple Petersen graph. As an essential component of folded Petersen cube, folded Petersen graph has many important properties. In this paper, we prove that the 3k-wide diameter and 3k-fault diameter of k-dimensional folded Petersen graph is either 2k + 1 or 2k + 2. Furthermore, we show that FPk is interval m...

On Some Flag-Transitive Extensions of the Dual Petersen Graph

We consider flag-transitive extensions of the dual Petersen graph satisfying one of the following "pathological" properties: (-riLL) there are pairs of collinear points incident to more than one line; ( -TT) there are triples of collinear points not incident to the same plane. We prove that ihere is just one example-satisfying (~LL), with six points and $6 as its au tomorphism group, and there ...

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...

Jacobsthal numbers in generalised Petersen graphs

We prove that the number of 1-factorisations of a generalised Petersen graph of the type GP (3k, k) is equal to the kth Jacobsthal number J(k) if k is odd, and equal to 4J(k), when k is even. Moreover, we verify the list colouring conjecture for GP (3k, k).

On the Relation between the Petersen Graph