Divisible design graphs
TL;DR: A divisible design graph as discussed by the authors is a graph whose adjacency matrix is the incidence matrix of a divisible graph, and is a generalization of (v,k,@l)-graphs.
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About: This article is published in Journal of Combinatorial Theory, Series A. The article was published on 01 Apr 2011. and is currently open access. The article focuses on the topics: Adjacency matrix & Strongly regular graph.
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Citations
Spreads in strongly regular graphs
Willem H. Haemers,Vladimir D. Tonchev +1 more
- 01 Jan 1995
TL;DR: A spread of a strongly regular graph is a partition of the vertex set into cliques that meet Delsarte's bound (alsocalled Hoffman's bound), which gives lower bounds for the number of non-isomorphic strongly regular graphs in the switching class of the regular two-graph.
42
2-Walk-Regular Dihedrants from Group-Divisible Designs
TL;DR: In this paper, the authors constructed bipartite $2$-walk-regular graphs with exactly 6 distinct eigenvalues as the point-block incidence graphs of group divisible designs with the dual property and showed that they are 2-arc-transitive dihedrants.
•Posted Content
2-walk-regular dihedrants from group-divisible designs
TL;DR: This note constructs bipartite 2-walk-regular graphs with exactly 6 distinct eigenvalues as incidence graphs of group-divisible designs with the dual property, and shows that they are 2-arc-transitive dihedrants.
11
On divisible design Cayley graphs
Vladislav V. Kabanov,Leonid Shalaginov +1 more
- 19 Feb 2020
TL;DR: In this paper, it was shown that divisible design Cayley graphs arise only by means of divisible difference sets relative to some subgroup, and that a special set in an affine group over a finite field is a divisible Cayley graph.
References
•Book
Symmetric Designs: An Algebraic Approach
Eric S. Lander
- 28 Feb 1983
TL;DR: In this article, the authors present some of the algebraic techniques that have been brought to bear on the question of existence, construction and symmetry of symmetric designs, including methods inspired by algebraic theory of coding and by representation theory of finite groups.
385
Strongly Regular Graphs
AE Andries Brouwer
- 01 Jan 2012
TL;DR: In this paper, a graph (simple, undirected, and loopless) of order v is called strongly regular with parameters v, k,λ,μ whenever it is not complete or edgeless.
Small regular graphs with four eigenvalues
Edwin van Dam,Edward Spence +1 more
TL;DR: For most feasible spectra of connected regular graphs with four distinct eigenvalues and at most 30 vertices the authors find all such graphs, using both theoretic and computer results.
78
Spreads in Strongly Regular Graphs
TL;DR: A spread of a strongly regular graph is a partition of the vertex set into cliques that meet Delsarte's bound (also called Hoffman's bound), which gives rise to colorings meeting Hoffman's lower bound for the chromatic number.
Spreads in strongly regular graphs
Willem H. Haemers,Vladimir D. Tonchev +1 more
- 01 Jan 1995
TL;DR: A spread of a strongly regular graph is a partition of the vertex set into cliques that meet Delsarte's bound (alsocalled Hoffman's bound), which gives lower bounds for the number of non-isomorphic strongly regular graphs in the switching class of the regular two-graph.
42
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