We show that the cop number of every generalized Petersen graph is at most 4. The strategy is to play a modified game of cops and robbers on an infinite cyclic covering space where the objective is to capture the robber or force the robber towards an end of the infinite graph. We prove that finite isometric subtrees are 1-guardable and apply this to determine the exact cop number of some famili...

Let G = (V, E) be a graph. A subset S ⊆ V is a dominating set of G, if every vertex u ∈ V − S is dominated by some vertex v ∈ S. The domination number, denoted by γ(G), is the minimum cardinality of a dominating set. For the generalized Petersen graph G(n), Behzad et al. [A. Behzad, M. Behzad, C.E. Praeger, On the domination number of the generalized Petersen graphs, Discrete Mathematics 308 (2...

Given a graph G, an independent set I(G) is a subset of the vertices of G such that no two vertices in I(G) are adjacent. The independence number α(G) is the order of a largest set of independent vertices. In this paper, we study the independence number for the Generalized Petersen graphs, finding both sharp bounds and exact results for subclasses of the Generalized Petersen graphs.

Dominating -color number of a graph is defined as the maximum number of color classes which are dominating sets of and is denoted by d, where the maximum is taken over all -coloring of . In this paper, we discussed the dominating -color number of Generalized Petersen Graphs. We have also discussed the condition under which chromatic number equals dominating -color number of Generalized Pet...

We establish some preliminary results for Sutner’s σ game, i.e. “Lights Out,” played on the generalized Petersen graph P (n, k). While all regular Petersen graphs admit game configurations that are not solvable, we prove that every game on the P (2n, n) graph has a unique solution. Moreover, we introduce an exceedingly simple strategy for finding the solution to any game on these graphs. Surpri...

In this paper, we completely describe the spectrum of the generalized Petersen graph P (n, k), thus adding to the classes of graphs whose spectrum is completely known.

In this paper we establish a theorem on the maximum number of vertices of a generalized Petersen graph as a function of the diameter.

Let G be a simple non-complete graph of order n. The r-component edge connectivity of G denoted as λr(G) is the minimum number of edges that must be removed from G in order to obtain a graph with (at least) r connected components. The concept of r-component edge connectivity generalizes that of edge connectivity by taking into account the number of components of the resulting graph. In this pap...

The crossing number of a graph is the least number of crossings of edges among all drawings of the graph in the plane. In this article, we prove that the crossing number of the generalized Petersen graph P (10, 3) is equal to 6.

We present several new constructions for small generalized polygons using small projective planes together with a conic or a unital, using other small polygons, and using certain graphs such as the Coxeter graph and the Pappus graph. We also give a new construction of the tilde geometry using the Petersen graph. 2001 Academic Press