Concept

# Generalized Petersen graph

Summary
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. Definition and notation In Watkins' notation, G(n, k) is a graph with vertex set :{u_0, u_1, \ldots, u_{n-1}, v_0, v_1, \ldots, v_{n-1}} and edge set :{u_iu_{i+1}, u_iv_i, v_iv_{i+k} \mid 0 \le i \le n-1 } where subscripts are to be read modulo n and k < n/2. Some authors use the notation GPG(n, k). Coxeter's notation for the same graph would be {n} + {n/k}, a combination of the Schläfli symbols for the regular n-gon and star polygon from which the graph is formed. The Petersen graph itself is G(5, 2) or {5} + {5/2}. Any generalized P
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