Uniqueness of strongly regular graphs having minimal \(p\)-rank

DOI10.1016/0024-3795(95)00184-SzbMath0831.05066MaRDI QIDQ1899393

René Peeters

Publication date: 12 February 1996

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

zbMATH Keywords

strongly regular graphgeneralized quadranglesadjacency matrix\(p\)-rankPaley graphscollinearity graphssymplectic graphslatin square graphs

Mathematics Subject Classification ID

Association schemes, strongly regular graphs (05E30) Orthogonal arrays, Latin squares, Room squares (05B15) Generalized quadrangles and generalized polygons in finite geometry (51E12) Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Triple systems (05B07) Isomorphism problems in graph theory (reconstruction conjecture, etc.) and homomorphisms (subgraph embedding, etc.) (05C60)

Related Items (10)

Switched symplectic graphs and their 2-ranks ⋮ Pseudo-Paley graphs and skew Hadamard difference sets from presemifields ⋮ Interlacing eigenvalues and graphs ⋮ Modular adjacency algebras, standard representations, and \(p\)-ranks of cyclotomic association schemes ⋮ Binary codes of some strongly regular subgraphs of the McLaughlin graph ⋮ Switched graphs of some strongly regular graphs related to the symplectic graph ⋮ Enumeration of cospectral and coinvariant graphs ⋮ On modular standard modules of association schemes ⋮ Graph switching, 2-ranks, and graphical Hadamard matrices ⋮ On the \(p\)-ranks of the adjacency matrices of distance-regular graphs

Cites Work

• On the \(p\)-rank of the adjacency matrices of strongly regular graphs
• On the p-rank of the incidence matrix of a balanced or partially balanced incomplete block design and its applications to error correcting codes
• Notes on binary codes related to the \(\mathrm{O}(5,q)\) generalized quadrangle for odd \(q\)
• Locally cotriangular graphs
• Bruck nets, codes, and characters of loops
• Structure and uniqueness of the \((81,20,1,6)\) strongly regular graph
• On the BIB design having the minimum p-rank
• On construction and identification of graphs. With contributions by A. Lehman, G. M. Adelson-Velsky, V. Arlazarov, I. Faragev, A. Uskov, I. Zuev, M. Rosenfeld and B. Weisfeiler
• Strongly regular graphs that are locally a disjoint union of hexagons
• Interlacing eigenvalues and graphs
• Strongly regular graphs, partial geometries and partially balanced designs
• SYMMETRIC HADAMARD MATRICES OF ORDER 36
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