Note on the girth of Ramanujan graphs

DOI10.1016/0095-8956(90)90026-VzbMath0708.05032OpenAlexW2073266670MaRDI QIDQ920107

A. G. Boshier, Norman L. Biggs

Publication date: 1990

Published in: Journal of Combinatorial Theory. Series B (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0095-8956(90)90026-v

zbMATH Keywords

eigenvaluesgirthexpandersRamanujan graph

Mathematics Subject Classification ID

Paths and cycles (05C38)

Related Items (14)

Quantum ergodicity for quantum graphs without back-scattering ⋮ Explicit construction of graphs with an arbitrary large girth and of large size ⋮ Isoperimetric numbers of graphs ⋮ Local-Global Phenomena in Graphs ⋮ On an anti‐Ramsey property of Ramanujan graphs ⋮ Impediments to diffusion in quantum graphs: Geometry-based upper bounds on the spectral gap ⋮ A new series of dense graphs of high girth ⋮ Low Polynomial Exclusion of Planar Graph Patterns ⋮ Keyed hash function from large girth expander graphs ⋮ On the limitations of the use of solvable groups in Cayley graph cage constructions ⋮ On the girth of random Cayley graphs ⋮ On the homogeneous algebraic graphs of large girth and their applications ⋮ Expander graphs based on GRH with an application to elliptic curve cryptography ⋮ Kissing numbers of regular graphs

Cites Work

• The sextet construction for cubic graphs
• Girths of bipartite sextet graphs
• Ramanujan graphs
• Explicit constructions of linear-sized superconcentrators
• Explicit constructions of graphs without short cycles and low density codes

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