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...

As a standard notation, assume that G = G(V,E) is a finite, simple and undirected graph with p vertices and q edges. A labeling of a graph is any mapping that sends some set of graph elements to a set of numbers (usually positive integers). If the domain is the vertex-set or the edge-set, the labelings are called respectively vertex-labelings or edge-labelings. If the domain is V ∪E then we cal...

GraphsG andH are T -equivalent if they have the same Tutte polynomial. G is T -unique if any arbitrary graph H being T -equivalent to G implies that H is isomorphic to G. We show that the generalized Petersen graph P (m, 2) and the line graph of P (m, 2) are T -unique. 1 The Tutte Polynomial Let G be a graph with vertex set V and edge set E, and let G[A] denote the subgraph ofG induced by the e...

Let G = (V (G),E(G)) be a simple finite undirected graph. A set S ⊆ V (G) is an independent set if no two vertices of S are adjacent. The independence number α(G) is the maximum cardinality of an independent set in G. In this paper, we investigate the independence number of generalized Petersen graph, and give the exact values of P(n,k) for k = 1,2,3,5.

Albertson and Collins defined the distinguishing number of a graph to be the smallest number of colors needed to color its vertices so that the coloring is preserved only by the identity automorphism. Collins and Trenk followed by defining the distinguishing chromatic number of a graph to be the smallest size of a coloring that is both proper and distinguishing. We show that, with two exception...

A connected graph G is said to be (a, d)-antimagic, for some positive integers a and d, if its edges admit a labeling by the integers 1,2, ... , IE( G) I such that the induced vertex labels consist of an arithmetic progression with the first term a and the common difference d. In this paper we prove that the generalized Petersen graph P(n,2) is (3n2+6, 3)-antimagic for n == 0 (mod 4), n ~ B.

In this paper we introduce a new order on the set of n-dimensional tuples and prove that this order preserves nestedness in the edge isoperimetric problem for the graph Pn, defined as the nth cartesian power of the well-known Petersen graph. The cutwidth and wirelength of Pn are also derived. These results are then generalized for the cartesian product of Pn and the m-dimensional binary hypercube.

‎The excessive index of a bridgeless cubic graph $G$ is the least integer $k$‎, ‎such that $G$ can be covered by $k$ perfect matchings‎. ‎An equivalent form of Fulkerson conjecture (due to Berge) is that every bridgeless‎ ‎cubic graph has excessive index at most five‎. ‎Clearly‎, ‎Petersen graph is a cyclically 4-edge-connected snark with excessive index at least 5‎, ‎so Fouquet and Vanherpe as...