Moore Graphs and Cycles Are Extremal Graphs for Convex Cycles

2014/11/12 by Jernej Azarija, Sandi Klavžar · 1 citation
Computer Science · Engineering · Mathematics · #Advanced Graph Theory Research #Interconnection Networks and Systems #graph theory and CDMA systems #Combinatorics #Mathematics #Graph #Regular polygon #Discrete mathematics #Chordal graph

paper · doi:10.1002/jgt.21837

openalex publication_date 2014/11/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/27

Abstract

Abstract Let denote the number of convex cycles of a simple graph G of order n , size m , and girth . It is proved that and that equality holds if and only if G is an even cycle or a Moore graph. The equality also holds for a possible Moore graph of diameter 2 and degree 57 thus giving a new characterization of Moore graphs.

Citations

• Algebraic Graph Theory
• On Moore Graphs with Diameters 2 and 3
• The Determinant of the Adjacency Matrix of a Graph

Cited by

• Moore graph [wikipedia]

Related

• Moore graphs and cycles are extremal graphs for convex cycles
• Isometric Cycles and a Generalization of Moore Graphs
• Convex Cycle Bases
• Cycle convexity and the tunnel number of links
• The Hypergraph Moore Bound