Two-Graphs, Switching Classes and Euler Graphs are Equal in Number

1975/06/01 by C. L. Mallows, N. J. A. Sloane · 3 citations
Mathematics · Computer Science · #Graph theory and applications #Cellular Automata and Applications #Interconnection Networks and Systems #Mathematics #Combinatorics #Chordal graph #Euler's formula #Discrete mathematics #Indifference graph #Maximal independent set #Euler number (physics) #1-planar graph #Graph #Euler equations #Semi-implicit Euler method #Backward Euler method #Mathematical analysis

paper · doi:10.1137/0128070

openalex publication_date 1975/06/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/06/11

Abstract

Seidel has shown that the number t_n of two-graphs on n nodes is equal to the number of switching classes of graphs on n nodes. Robinson, and independently Liskovec, have given an explicit formula for the number e_n of Euler graphs on n nodes. It is shown here that t_n = e_n for all n.

Cited by

• Cohomological aspects of two-graphs
• Equiangular lines in Euclidean spaces
• Eulerian path [wikipedia]