1971/09/01 by Roberto Frucht, Jack E. Graver, Mark E. Watkins · 195 citations
Computer Science · Engineering · Mathematics · #Advanced Graph Theory Research #Combinatorics #Coxeter group #Discrete mathematics #Finite Group Theory Research #Graph #Line graph #Mathematics #Modulo #Petersen graph #Vertex (graph theory) #Voltage graph #graph theory and CDMA systems
paper · doi:10.1017/s0305004100049811
published in Mathematical Proceedings of the Cambridge Philosophical Society 70(2), 211-218 (Cambridge University Press)
openalex publication_date 1971/09/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/06/11
1. Introduction . For integers n and k with 2 ≤ 2k < n , the generalized Petersen graph G(n, k) has been defined in (8) to have vertex-set and edge-set E(G(n, k)) to consist of all edges of the form where i is an integer. All subscripts in this paper are to be read modulo n , where the particular value of n will be clear from the context. Thus G(n, k) is always a trivalent graph of order 2 n , and G (5, 2) is the well known Petersen graph. (The subclass of these graphs with n and k relatively prime was first considered by Coxeter ((2), p. 417ff.).)