Moore graphs and cycles are extremal graphs for convex cycles

2012/10/23 by Jernej Azarija, Azarija, Jernej, Sandi Klavžar +1
Computer Science · Engineering · Mathematics · #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Limits and Structures in Graph Theory #graph theory and CDMA systems #math.CO

paper · pdf · doi:10.48550/arxiv.1210.6342

arxiv created 2012/10/23 · openalex publication_date 2012/10/23 · arxiv updated 2012/10/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let ρ(G) denote the number of convex cycles of a simple graph G of order n, size m, and girth 3 <= g <=n. It is proved that ρ(G) ≤ (n)/(g)(m-n+1) 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

• The Determinant of the Adjacency Matrix of a Graph

Related

• Isometric Cycles and a Generalization of Moore Graphs
• The Hypergraph Moore Bound
• Cycle convexity and the tunnel number of links
• Existence of a Moore graph of degree 57 is still open
• A Mixed Graph Achieving A Moore-like Bound