On the spanning connectivity of the generalized Petersen graphs P(n,3)

In this paper, we employed lattice model to describe the three internally vertex-disjoint paths that span the vertex set of the generalized Petersen graph P(n,3). We showed that the P(n,3) is 3-spanning connected for odd n. Based on the lattice model, five amalgamated and one extension mechanisms are introduced to recursively establish the 3-spanning connectivity of the P(n,3). In each amalgamated mechanism, a particular lattice trail was amalgamated with the lattice trails that was dismembered, transferred, or extended from parts of the lattice trails for P(n−6,3), where a lattice tail is a trail in the lattice model that represents a path in P(n,3).