A construction of small \((q-1)\)-regular graphs of girth 8

zbMath1310.05152arXiv1501.02452MaRDI QIDQ2341056

Marién Abreu, Gabriela Araujo-Pardo, Domenico Labbate, Camino Balbuena

Publication date: 22 April 2015

Published in: The Electronic Journal of Combinatorics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1501.02452

zbMATH Keywords

girthcagesMoore graphsperfect dominating sets

Mathematics Subject Classification ID

Extremal problems in graph theory (05C35) Vertex subsets with special properties (dominating sets, independent sets, cliques, etc.) (05C69)

Related Items (5)

On the automorphisms of a family of small q-regular graphs of girth 8 ⋮ Special structures in \(\mathcal{Q}(4, q)\), projective planes and its application in \(L(h, k)\)-colorings of their Moore graphs ⋮ On the packing chromatic number of Moore graphs ⋮ An alternate description of a (q + 1, 8)-cage ⋮ Small regular graphs of girth 7

Uses Software

• GENREG

Cites Work

• Families of small regular graphs of girth 5
• A family of regular graphs of girth 5
• Finding small regular graphs of girths 6, 8 and 12 as subgraphs of cages
• New upper bounds on the order of cages
• A simple method for constructing small cubic graphs of girths 14, 15, and 16
• Dynamic cage survey
• Affine representations of generalized quadrangles
• Regular graphs constructed from the classical generalized quadrangle Q(4, q)
• Incidence Matrices of Projective Planes and of Some Regular Bipartite Graphs of Girth 6 with Few Vertices
• The smallest graph of girth 6 and valency 7
• Fast generation of regular graphs and construction of cages
• Minimal Regular Graphs of Girths Eight and Twelve
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