Pick's inequality and tournaments

DOI10.1016/0024-3795(93)90281-RzbMath0776.05072MaRDI QIDQ1801444

David A. Gregory, Stephen J. Kirkland, Bryan L. Shader

Publication date: 21 July 1993

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

zbMATH Keywords

eigenvalueadjacency matrixtournamentPick's inequality

Mathematics Subject Classification ID

Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Directed graphs (digraphs), tournaments (05C20)

Related Items (18)

On the number of 7-cycles in regular \(n\)-tournaments ⋮ Eigenvalues of oriented-graph matrices ⋮ Extremal digraphs with given clique number ⋮ The idiosyncratic polynomial of digraphs ⋮ Solution of the conjecture of Brualdi and Li ⋮ Skew-adjacency matrices of graphs ⋮ Skew-adjacency matrices of tournaments with bounded principal minors ⋮ On the Laplacian spread of digraphs ⋮ Large regular bipartite graphs with median eigenvalue 1 ⋮ On the maximum skew spectral radius and minimum skew energy of tournaments ⋮ The skew energy of tournaments ⋮ Spectra of digraphs ⋮ On the location of the spectrum of hypertournament matrices ⋮ Spectral radii of tournament matrices whose graphs are related by an arc reversal ⋮ On 5-Cycles and 6-Cycles in Regular n-Tournaments ⋮ Some properties complementary to Brualdi-Li matrices ⋮ Tournament matrices with extremal spectral properties ⋮ \(k\)-spectrally monomorphic tournaments

Cites Work

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• On tournament matrices
• Algebraic multiplicity of the eigenvalues of a tournament matrix
• Recent results in the theory of graph spectra
• Tournament matrices with extremal spectral properties
• Inequalities of compound and induces matrices with applications to combinatorial analysis
• Some remarks on tournament matrices
• Tournament matrices and their generalizations, I.
• Vertex-switching, isomorphism, and pseudosimilarity
• Hypertournament matrices, score vectors and eigenvalues
• Every one a Winner or how to Avoid Isomorphism Search when Cataloguing Combinatorial Configurations
• Tournament games and positive tournaments
• On the characteristic roots of tournament matrices
• On Generalized Tournament Matrices

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