The generalized Petersen graphs (GPGs) which have been invented by Watkins, may serve for perhaps the simplest nontrivial examples of “galactic” graphs, i.e. those with a nice property of having a semiregular automorphism. Some of them are also vertextransitive or even more highly symmetric, and some are Cayley graphs. In this paper, we study a further extension of the notion of GPGs with the e...

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...

Generalized Petersen graphs are commonly used interconnection networks, and wide diameter is an important parameter to measure fault-tolerance and efficiency of parallel processing computer networks. In this paper, we show that the diameter and 3-wide diameter of generalized Petersen graph P (m,a) are both O( m 2a ), where a ≥ 3.

We give explicit and efficiently computable formulas for the number of isomorphism classes of I-graphs, connected I-graphs, and generalized Petersen graphs. The tool that we use is the well-known Cauchy-FrobeniusBurnside lemma.