Random strongly regular graphs
TL;DR: This paper develops no general theory, but explores a few examples and techniques which can be applied in some cases and concludes with some speculation about ''random jumbled graphs''.
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About: This article is published in Discrete Mathematics. The article was published on 01 Dec 2003. and is currently open access. The article focuses on the topics: Strongly regular graph & Random graph.
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Citations
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.
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The search for N-e.c. graphs
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On a conjecture of Brouwer involving the connectivity of strongly regular graphs
TL;DR: It is proved that Andries E. Brouwer's conjecture regarding the minimum number of vertices of a strongly regular graph whose removal disconnects the graph into non-singleton components is true for many families of strongly regular graphs.
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Disconnecting strongly regular graphs
TL;DR: It is shown that the minimum number of vertices whose removal disconnects a connected strongly regular graph into non-singleton components equals the size of the neighborhood of an edge for many graphs.
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Identifying Codes in Vertex-Transitive Graphs and Strongly Regular Graphs
TL;DR: This work exhibits infinite families of vertex-transitive graphs with integer and fractional identifying codes of order |V|^a with a in {1/4,1/3,2/5}.
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References
•Book
Theory of Groups of Finite Order
William Snow Burnside
- 01 Jan 1955
TL;DR: In this article, the authors define the notion of permutation groups as a group of linear substitutions, and show that a group can be represented as a permutation-group.
•Book
Permutation groups
Peter J. Cameron
- 01 Mar 1996
Abstract: Loading takes about thirteen minutes, half that time due to builtin pauses. summary The set of all permutations of a set is a group under composition. binary closure In this section it is shown that bij[x, x] is binary closed under COMPOSE. Lemma.
1.2K
Surveys in Combinatorics, 1999: Models of Random Regular Graphs
Nicholas Charles Wormald
- 01 Jan 1999
TL;DR: This is a survey of results on properties of random regular graphs, together with an exposition of some of the main methods of obtaining these results.
804
Strongly regular graphs, partial geometries and partially balanced designs.
TL;DR: In this article, the concept of a partial geometry is introduced, which serves to unify and generalize certain theorems on embedding of nets, and uniqueness of association schemes of partially balanced designs, by Bruck, Connor, Shrikhande and others.