Distance-regular graphs with diameter 3 and eigenvalue \(a_2 - c_3\)

DOI10.1016/j.laa.2019.10.021zbMath1437.05240OpenAlexW2985427725MaRDI QIDQ2174419

Masood Ur Rehman, Jongyook Park, Jack H. Koolen, Quaid Iqbal

Publication date: 21 April 2020

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

Full work available at URL: https://doi.org/10.1016/j.laa.2019.10.021

zbMATH Keywords

strongly regular graphsdistance-regular graphseigenvaluesgeometricdistance-\(i\) graphs

Mathematics Subject Classification ID

Association schemes, strongly regular graphs (05E30) Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Distance in graphs (05C12)

Related Items (3)

ON DISTANCE–REGULAR GRAPHS OF DIAMETER 3 WITH EIGENVALUE \(\theta=1\) ⋮ On bounding the diameter of a distance-regular graph ⋮ A characterization of graphs with regular distance-2 graphs

Cites Work

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• Distance-regular graphs
• Distance-regular graphs with or at least half the valency
• Distance regular graphs of diameter 3 and strongly regular graphs
• Using equality in the Krein conditions to prove nonexistence of certain distance-regular graphs
• Finite generalized quadrangles
• Some elementary inequalities for distance-regular graphs
• Strongly regular graphs with smallest eigenvalue -m
• The smallest eigenvalues of Hamming graphs, Johnson graphs and other distance-regular graphs with classical parameters
• Chromatic number and the 2-rank of a graph
• A new distance-regular graph of diameter 3 on 1024 vertices
• Distance-regular graphs of diameter 3 having eigenvalue \(-1\)
• The spectral excess theorem for graphs with few eigenvalues whose distance-2 or distance-1-or-2 graph is strongly regular

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