Generalized Petersen graph

In graph theory, the generalized Petersen graphs are a family of cubic graphs formed by connecting the vertices of a regular polygon to the corresponding vertices of a star polygon. They include the Petersen graph and generalize one of the ways of constructing the Petersen graph. The generalized Petersen graph family was introduced in 1950 by H. S. M. Coxeter and was given its name in 1969 by Mark Watkins.A 3-coloring of the Petersen graph or G ⁡ ( 5 , 2 ) {displaystyle operatorname {G} (5,2)} A 2-coloring of the Desargues graph or G ⁡ ( 10 , 3 ) {displaystyle operatorname {G} (10,3)} A 3-coloring of the Dürer graph or G ⁡ ( 6 , 2 ) {displaystyle operatorname {G} (6,2)} A 4-edge-coloring of the Petersen graph or G ⁡ ( 5 , 2 ) {displaystyle operatorname {G} (5,2)} A 3-edge-coloring of the Dürer graph or G ⁡ ( 6 , 2 ) {displaystyle operatorname {G} (6,2)} A 3-edge-coloring of the dodecahedron or G ⁡ ( 10 , 2 ) {displaystyle operatorname {G} (10,2)} A 3-edge-coloring of the Desargues graph or G ⁡ ( 10 , 3 ) {displaystyle operatorname {G} (10,3)} A 3-edge-coloring of the Nauru graph or G ⁡ ( 12 , 5 ) {displaystyle operatorname {G} (12,5)} In graph theory, the generalized Petersen graphs are a family of cubic graphs formed by connecting the vertices of a regular polygon to the corresponding vertices of a star polygon. They include the Petersen graph and generalize one of the ways of constructing the Petersen graph. The generalized Petersen graph family was introduced in 1950 by H. S. M. Coxeter and was given its name in 1969 by Mark Watkins. In Watkins' notation, G(n,k) is a graphwith vertex set