Nonregular Graphs with Three Eigenvalues
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TL;DR: In this paper, the authors study nonregular graphs with three eigenvalues and determine all the ones with least eigenvalue 2, and give new infinite families of examples for these graphs.
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About: This article is published in Journal of Combinatorial Theory, Series B. The article was published on 01 Jul 1998. and is currently open access. The article focuses on the topics: Indifference graph & Chordal graph.
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Citations
Spectra of graphs
Andries E. Brouwer,Willem H. Haemers +1 more
- 01 Jan 2012
TL;DR: This book gives an elementary treatment of the basic material about graph Spectra, both for ordinary, and Laplace and Seidel spectra, by covering standard topics before presenting some new material on trees, strongly regular graphs, two-graphs, association schemes, p-ranks of configurations and similar topics.
Which graphs are determined by their spectrum
Edwin van Dam,Willem H. Haemers +1 more
TL;DR: For almost all graphs the answer to the question in the title is still unknown as mentioned in this paper, and the cases for which the answer is known are surveyed in the survey of cases where the Laplacian matrix is known.
747
•Book
Topics in Graph Automorphisms and Reconstruction
Josef Lauri,Raffaele Scapellato +1 more
- 01 Mar 2003
TL;DR: In this paper, the authors present an in-depth coverage of important areas of graph theory maintaining a focus on symmetry properties of graphs, including graph automorphisms and the reconstruction problem.
180
On the distance spectrum of graphs
TL;DR: In this article, it was shown that the complete k-partite graph is determined by its D -spectrum, and that all connected graphs of diameter 2 have at least three D -eigenvalues when λ 1 (D ) is not an integer.
89
Graphs with four distinct Laplacian eigenvalues
TL;DR: In this article, the authors investigate connected nonregular graphs with four distinct Laplacian eigenvalues and characterize all such graphs which are bipartite or have exactly one multiple Laplacey eigenvalue.
References
•Book
Designs, graphs, codes, and their links
Peter J. Cameron,J.H. van Lint +1 more
- 01 Jan 1991
TL;DR: The authors have considerably reworked and expanded their earlier successful books on designs, graphs and codes, into an invaluable textbook that is accessible to any student with a background of undergraduate algebra.
559
A survey of two-graphs
J.J. Seidel
- 01 Jan 1976
TL;DR: In this article, a one-to-one correspondence between the two-graphs and the switching classes of graphs on the set of n elements is established, and the correspondence is shown to hold also for the binary maps with vanishing co-boundaries.
262
Line graphs, root systems, and elliptic geometry
TL;DR: In this paper, star-closed sets of lines at 60° and 90° are discussed, leading to a theorem that leaves only a restricted number of possibilities, of a specific structure.
234
Strongly regular graphs and partial geometries
J.H. van Lint,Andries E. Brouwer +1 more
- 01 Jan 1984
TL;DR: Brouwer and van Lint as mentioned in this paper gave a survey of recent results concerning construction, uniqueness or nonexistence of strongly regular graphs and partial geometries and restricted themselves to results which did not occur in the well known earlier surveys.
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