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.

It is well-known that each nonnegative integral flow of a directed graph can be decomposed into a sum of nonnegative graph circuit flows, which cannot be further decomposed into nonnegative integral sub-flows. This is equivalent to saying that indecomposable flows of graphs are those graph circuit flows. Turning from graphs to signed graphs, the indecomposable flows are much richer than that of...

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

We define the signed Cayley graph on Xn denoted by Sn, and study several properties such as balancing, clusterability sign-compatibility of Sn. Apart from it we also characterization canonical consistency for some n.