Journal ArticleDOI
A note on cospectral graphs
TLDR
It is shown that in many instances this adjacency matrix is superior to the usual (0, 1) adjacencies, and will distinguish cospectral pairs, when the latter will not.About:
This article is published in Journal of Combinatorial Theory, Series B.The article was published on 1980-02-01. It has received 77 citations till now. The article focuses on the topics: Seidel adjacency matrix & Integer matrix.read more
Citations
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BookDOI
Spectra of graphs
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.
Journal ArticleDOI
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.
Posted Content
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.
Journal ArticleDOI
Developments on spectral characterizations of graphs
Edwin van Dam,Willem H. Haemers +1 more
TL;DR: In this paper, van Dam et al. gave a survey of answers to the question of which graphs are determined by the spectrum of some matrix associated to the graph and formulated some research questions on the topic.
Journal ArticleDOI
Enumeration of cospectral graphs
Willem H. Haemers,Edward Spence +1 more
TL;DR: It turns out that for the enumerated cases a large part of allcospectral graphs comes from GM switching, and that the fraction of graphs on n vertices with a cospectral mate starts to decrease at some value of n < 11 (depending on the matrix).
References
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Journal ArticleDOI
An Efficient Algorithm for Graph Isomorphism
Derek G. Corneil,C. C. Gotlieb +1 more
TL;DR: It is shown that the re ordered graphs form a sufficiency condition for isomorphism; namely, if the reordered graphs are identical, then the given graphs are isomorphic.
Journal ArticleDOI
The characteristic polynomial of a graph
TL;DR: In this article, the problem of determining under what conditions the characteristic polynomial of the adjacency matrix of a graph distinguishes between non-isomorphic graphs is addressed, and a formula for the coefficients of the polynomials of an arbitrary digraph is derived.
Journal ArticleDOI
Cospectral Graphs and Digraphs
TL;DR: The conjecture was promptly shot down by a member of the audience (R. C. Bose), who produced a counter-example that the conjecture was not true, since Collatz and Sinogowitz had displayed two different trees with 8 nodes having the same characteristic polynomial as discussed by the authors.
Book ChapterDOI
Exactly thirteen connected cubic graphs have integral spectra
TL;DR: In this article, it was shown that it is easy to find the seven connected cubic integral graphs with integral spectra, maximum degree at most three, and minimum degree less than three.