Distance-regularised graphs are distance-regular or distance-biregular

DOI10.1016/0095-8956(87)90027-XzbMath0616.05041OpenAlexW2012945176MaRDI QIDQ1821114

John Shawe-Taylor, Chris D. Godsil

Publication date: 1987

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(87)90027-x

zbMATH Keywords

distance-regular graphsdistance-biregulardistance-regularised graph

Mathematics Subject Classification ID

Graphs and abstract algebra (groups, rings, fields, etc.) (05C25)

Related Items (35)

A Spectral Moore Bound for Bipartite Semiregular Graphs ⋮ Distance mean-regular graphs ⋮ Coverings of complete bipartite graphs and associated structures ⋮ On strongly closed subgraphs of highly regular graphs ⋮ Quotients of association schemes ⋮ Automorphism groups of primitive distance-bitransitive graphs are almost simple ⋮ Intersection diagrams of distance-biregular graphs ⋮ On the 2-\(Y\)-homogeneous condition of the incidence graphs of 2-designs ⋮ From local adjacency polynomials to locally pseudo-distance-regular graphs ⋮ Semiregular graphs and their algebra ⋮ On the Terwilliger algebra of distance-biregular graphs ⋮ The spectral excess theorem for distance-biregular graphs. ⋮ The \(M\)-matrix group inverse problem for distance-biregular graphs ⋮ Completely regular clique graphs ⋮ A simple approach for lower-bounding the distortion in any hyperbolic embedding ⋮ A \(Q\)-polynomial structure associated with the projective geometry \(L_N (q)\) ⋮ Continuous time quantum walks on graphs: group state transfer ⋮ Pseudo-distance-regularized graphs are distance-regular or distance-biregular ⋮ State transfer on graphs ⋮ The dual of Pasch's axiom ⋮ The subconstituent algebra of an association scheme. I ⋮ Distance regular covers of the complete graph ⋮ Algebraic characterizations of graph regularity conditions ⋮ Edge-distance-regular graphs ⋮ Unnamed Item ⋮ Classification of Ryser graphs ⋮ On the distance spectrum of minimal cages and associated distance biregular graphs ⋮ Current research on algebraic combinatorics. Supplements to our book, Algebraic combinatorics I ⋮ Characterizing imprimitive partition designs of binary Hamming graphs ⋮ Locally s-distance transitive graphs ⋮ Distance-biregular graphs with 2-valent vertices and distance regular line graphs ⋮ On (almost) \(2\)-\(Y\)-homogeneous distance-biregular graphs ⋮ A general method to obtain the spectrum and local spectra of a graph from its regular partitions ⋮ Completely regular clique graphs. II ⋮ Spectrally extremal vertices, strong cospectrality, and state transfer

Cites Work

• Unnamed Item
• Generalized n-gons and Chebyshev polynomials
• Distance-biregular graphs with 2-valent vertices and distance regular line graphs
• Automorphism groups of primitive distance-bitransitive graphs are almost simple
• Spectral conditions for the reconstructibility of a graph

This page was built for publication: Distance-regularised graphs are distance-regular or distance-biregular