A characterization of the components of the graphs \(D(k,q)\)

DOI10.1016/S0012-365X(96)83019-6zbMath0861.05051MaRDI QIDQ1924372

Felix Lazebnik, Vasiliy A. Ustimenko, Andrew J. Woldar

Publication date: 4 May 1997

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

zbMATH Keywords

automorphism groupcharacterizationgirthcomponentsextremal graphgraphs \(D(k,q)\)

Mathematics Subject Classification ID

Structural characterization of families of graphs (05C75)

Related Items (20)

On the conjecture for the girth of the bipartite graph \(D(k,q)\) ⋮ A Hierarchy of Lower Bounds for Sublinear Additive Spanners ⋮ The eigenvalues of the graphs \(D(4,q)\) ⋮ On the girth of the bipartite graph \(D(k, q)\) ⋮ Girth of the algebraic bipartite graph \(D(k,q)\) ⋮ A simple proof for the lower bound of the girth of graphs \(D(n,q)\) ⋮ On the girth cycles of the bipartite graph \(D(k, q)\) ⋮ On the eigenvalues of the graphs \(D(5,q)\) ⋮ On New Examples of Families of Multivariate Stable Maps and their Cryptographical Applications ⋮ On the key expansion of \(D(n, K)\)-based cryptographical algorithm ⋮ On LDPC codes corresponding to affine parts of generalized polygons ⋮ Dynamical systems as the main instrument for the constructions of new quadratic families and their usage in cryptography ⋮ On the connectivity of certain graphs of high girth. ⋮ LDPC Codes Based on Algebraic Graphs ⋮ General properties of some families of graphs defined by systems of equations ⋮ Improved Guarantees for Vertex Sparsification in Planar Graphs ⋮ On the homogeneous algebraic graphs of large girth and their applications ⋮ Polarities and \(2k\)-cycle-free graphs ⋮ On the key exchange and multivariate encryption with nonlinear polynomial maps of stable degree ⋮ Extremal properties of regular and affine generalized \(m\)-gons as tactical configurations

Cites Work

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• Explicit group-theoretical constructions of combinatorial schemes and their application to the design of expanders and concentrators
• Ramanujan graphs
• New examples of graphs without small cycles and of large size
• Explicit construction of graphs with an arbitrary large girth and of large size
• Graphs of prescribed girth and bi-degree
• A new series of dense graphs of high girth

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