On Dihedral Flows of Generalized Petersen Graphs Cellularly Embedded in Closed Orientable Surfaces
Francis Yap, Tjaart Jan B. Estrada, Priscilla Supnet Macansantos · Matemática Contemporânea · 2022
Let G be a graph and S be a closed orientable surface.Litjens defined G to have a nowhere-identity dihedral 4-flow if for each S in which G can be cellularly embedded, there is a rotation system π of G which gives a nowhere-identity dihedral 4-flow [4].Furthermore, he proved the existence of nowhere-identity dihedral 4flows for bridgeless cubic graphs with 16 or less vertices.We give a method for exhibiting the nowhere-identity dihedral n-flows in generalized Petersen graphs and illustrate the results by exhibiting the nowhere-identity dihedral 4-flows of G(3, 1).