A simple proof for the lower bound of the girth of graphs \(D(n,q)\)

DOI10.1016/j.disc.2023.113705zbMath1525.05089arXiv2212.13096OpenAlexW4387113059MaRDI QIDQ6080170

Vladislav Taranchuk

Publication date: 30 October 2023

Published in: Discrete Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2212.13096

zbMATH Keywords

Turán numbersalgebraically defined graphshigh girth

Mathematics Subject Classification ID

Extremal problems in graph theory (05C35) Enumeration in graph theory (05C30) Paths and cycles (05C38) Distance in graphs (05C12)

Cites Work

• On the conjecture for the girth of the bipartite graph \(D(k,q)\)
• On the girth of the bipartite graph \(D(k, q)\)
• On the spectrum of Wenger graphs
• Explicit group-theoretical constructions of combinatorial schemes and their application to the design of expanders and concentrators
• Ramanujan graphs
• Existence and explicit constructions of \(q+1\) regular Ramanujan graphs for every prime power \(q\)
• The Moore bound for irregular graphs
• On the connectivity of certain graphs of high girth.
• Cycles of even length in graphs
• Explicit construction of graphs with an arbitrary large girth and of large size
• Graphs of prescribed girth and bi-degree
• A characterization of the components of the graphs \(D(k,q)\)
• The eigenvalues of the graphs \(D(4,q)\)
• General properties of some families of graphs defined by systems of equations
• Recent Developments in Low-Density Parity-Check Codes
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