The Electronic Journal of Combinatorics: EJC, ISSN 1097-1440, 04/2016, Volume Dynamic Surveys, pp. 1 - 156

This is a survey of distance-regular graphs. We present an introduction to distance-regular graphs for the reader who is unfamiliar with the subject, and then...

Q-RACAH TYPE | MATHEMATICS, APPLIED | association scheme | BILINEAR-FORMS GRAPHS | DIMENSIONAL IRREDUCIBLE MODULES | SEMIDEFINITE PROGRAMMING RELAXATIONS | Distance-regulargraph | P-polynomial | SPECTRAL EXCESS THEOREM | LIEBLER LINE CLASSES | MATHEMATICS | STRONGLY CLOSED SUBGRAPHS | geometric | DUAL POLAR GRAPHS | survey | Q-polynomial | POLYNOMIAL ASSOCIATION SCHEMES | MODULAR ADJACENCY ALGEBRAS

Q-RACAH TYPE | MATHEMATICS, APPLIED | association scheme | BILINEAR-FORMS GRAPHS | DIMENSIONAL IRREDUCIBLE MODULES | SEMIDEFINITE PROGRAMMING RELAXATIONS | Distance-regulargraph | P-polynomial | SPECTRAL EXCESS THEOREM | LIEBLER LINE CLASSES | MATHEMATICS | STRONGLY CLOSED SUBGRAPHS | geometric | DUAL POLAR GRAPHS | survey | Q-polynomial | POLYNOMIAL ASSOCIATION SCHEMES | MODULAR ADJACENCY ALGEBRAS

Journal Article

Graphs and Combinatorics, ISSN 0911-0119, 7/2018, Volume 34, Issue 4, pp. 555 - 570

A generalized strongly regular graph of grade p, as a generalization of strongly regular graphs, is a regular graph such that the number of common neighbours...

05E30 | 15A42 | Semi-strongly regular graph | 05C50 | Quasi-strongly regular graph | Mathematics | Engineering Design | Combinatorics | Strongly regular graph | Cayley graph | Deza graph | Association scheme | MATHEMATICS | Information science | Yuan (China) | Eigenvalues | Graphs | Inequalities | Eigen values

05E30 | 15A42 | Semi-strongly regular graph | 05C50 | Quasi-strongly regular graph | Mathematics | Engineering Design | Combinatorics | Strongly regular graph | Cayley graph | Deza graph | Association scheme | MATHEMATICS | Information science | Yuan (China) | Eigenvalues | Graphs | Inequalities | Eigen values

Journal Article

Journal of Algebraic Combinatorics, ISSN 0925-9899, 6/2018, Volume 47, Issue 4, pp. 623 - 639

We generalize the concept of strong walk-regularity to directed graphs. We call a digraph strongly $$\ell $$ ℓ -walk-regular with $$\ell > 1$$ ℓ>1 if the...

Walk | 05E30 | Strongly regular digraph | 05C50 | Convex and Discrete Geometry | Eigenvalues | Mathematics | Order, Lattices, Ordered Algebraic Structures | Group Theory and Generalizations | Combinatorics | Computer Science, general | Spectrum | MATHEMATICS | DIGRAPHS | Management science | Graphs | Graph theory | Eigen values | Mathematics - Combinatorics

Walk | 05E30 | Strongly regular digraph | 05C50 | Convex and Discrete Geometry | Eigenvalues | Mathematics | Order, Lattices, Ordered Algebraic Structures | Group Theory and Generalizations | Combinatorics | Computer Science, general | Spectrum | MATHEMATICS | DIGRAPHS | Management science | Graphs | Graph theory | Eigen values | Mathematics - Combinatorics

Journal Article

Discrete Mathematics, ISSN 0012-365X, 10/2019, Volume 342, Issue 10, pp. 2818 - 2820

We exhibit a new construction of edge-regular graphs with regular cliques that are not strongly regular. The infinite family of graphs resulting from this...

Regular clique | Strongly regular graph | Edge-regular graph

Regular clique | Strongly regular graph | Edge-regular graph

Journal Article

Linear Algebra and Its Applications, ISSN 0024-3795, 11/2019, Volume 580, pp. 464 - 474

We show that the strongly regular graph on non-isotropic points of one type of the polar spaces of type , , , , and are not determined by its parameters for ....

Strongly regular graph | Switching | Polar space | Spectrum | Analysis | Algebra

Strongly regular graph | Switching | Polar space | Spectrum | Analysis | Algebra

Journal Article

Graphs and Combinatorics, ISSN 0911-0119, 2019

Journal Article

Discrete Mathematics, ISSN 0012-365X, 06/2017, Volume 340, Issue 6, pp. 1367 - 1373

In this paper, we study 24 possibilities of directed strongly regular graphs with adjacency matrix of rank 6, our proof is based on two effective algorithms....

Rank of matrix | Directed strongly regular graphs | Adjacency matrix | MATHEMATICS | Algorithms

Rank of matrix | Directed strongly regular graphs | Adjacency matrix | MATHEMATICS | Algorithms

Journal Article

Designs, Codes and Cryptography, ISSN 0925-1022, 12/2017, Volume 85, Issue 3, pp. 457 - 470

If s is an even power of a prime and t equals s or $$s\sqrt{s}$$ s s , we show the existence of pseudo-geometric strongly regular graphs having the same...

05E30 | Information and Communication, Circuits | Generalized quadrangles | 51A50 | Data Encryption | 05C62 | Mathematics | Primary 51E20 | Strongly regular graphs | Secondary 51E12 | Data Structures, Cryptology and Information Theory | Discrete Mathematics in Computer Science | Coding and Information Theory | Combinatorics | Projective geometry | MATHEMATICS, APPLIED | COMPUTER SCIENCE, THEORY & METHODS | Graphs

05E30 | Information and Communication, Circuits | Generalized quadrangles | 51A50 | Data Encryption | 05C62 | Mathematics | Primary 51E20 | Strongly regular graphs | Secondary 51E12 | Data Structures, Cryptology and Information Theory | Discrete Mathematics in Computer Science | Coding and Information Theory | Combinatorics | Projective geometry | MATHEMATICS, APPLIED | COMPUTER SCIENCE, THEORY & METHODS | Graphs

Journal Article

Electronic Notes in Discrete Mathematics, ISSN 1571-0653, 10/2016, Volume 54, pp. 271 - 276

We prove that if and are primitive strongly regular graphs with the same parameters and is a homomorphism from to , then is either an isomorphism or a coloring...

graph homomorphisms | strongly regular graphs | cores | Lovász theta

graph homomorphisms | strongly regular graphs | cores | Lovász theta

Journal Article

Journal of Algebraic Combinatorics, ISSN 0925-9899, 12/2017, Volume 46, Issue 3, pp. 571 - 588

Let $$\varGamma $$ Γ be a distance-regular graph with diameter $$d \ge 2$$ d ≥ 2 . It is said to have classical parameters $$(d, b, \alpha , \beta )$$ ( d , b...

Distance-regular graphs | Convex and Discrete Geometry | Formally self-dual | Mathematics | Order, Lattices, Ordered Algebraic Structures | Group Theory and Generalizations | Combinatorics | Computer Science, general | Classical parameters | Locally strongly regular | Tight graphs | FORMS | MATHEMATICS | ASSOCIATION SCHEMES | Information science | Cubes | Graphs | Partitions

Distance-regular graphs | Convex and Discrete Geometry | Formally self-dual | Mathematics | Order, Lattices, Ordered Algebraic Structures | Group Theory and Generalizations | Combinatorics | Computer Science, general | Classical parameters | Locally strongly regular | Tight graphs | FORMS | MATHEMATICS | ASSOCIATION SCHEMES | Information science | Cubes | Graphs | Partitions

Journal Article

Journal of Combinatorial Theory, Series A, ISSN 0097-3165, 05/2013, Volume 120, Issue 4, pp. 803 - 810

We study a generalization of strongly regular graphs. We call a graph strongly walk-regular if there is an such that the number of walks of length from a...

Walks | Strongly regular graphs | Spectrum | MATHEMATICS | 4 EIGENVALUES | Mathematics - Combinatorics

Walks | Strongly regular graphs | Spectrum | MATHEMATICS | 4 EIGENVALUES | Mathematics - Combinatorics

Journal Article

Linear Algebra and Its Applications, ISSN 0024-3795, 11/2018, Volume 557, pp. 62 - 83

We show that there is no strongly regular graph. The result is obtained by a mix of algebraic and computational approaches. The main idea is to build large...

Eigenvalues | Star complement technique | Interlacing | Strongly regular graphs | MATHEMATICS | MATHEMATICS, APPLIED | Graphs | Graph theory | Algorithms | Linear algebra | Eigen values

Eigenvalues | Star complement technique | Interlacing | Strongly regular graphs | MATHEMATICS | MATHEMATICS, APPLIED | Graphs | Graph theory | Algorithms | Linear algebra | Eigen values

Journal Article

Discrete Mathematics, ISSN 0012-365X, 06/2015, Volume 338, Issue 6, pp. 1011 - 1016

A directed strongly regular graph with parameters is a -regular directed graph with vertices satisfying that the number of walks of length 2 from a vertex to a...

Computation in GAP | Moore graph | Directed strongly regular graph | MATHEMATICS | DIGRAPHS

Computation in GAP | Moore graph | Directed strongly regular graph | MATHEMATICS | DIGRAPHS

Journal Article

Discrete Mathematics, ISSN 0012-365X, 08/2019, Volume 342, Issue 8, pp. 2204 - 2212

In this paper we investigate bounds on set multipartite Ramsey numbers for the bipartite graph , extending or improving well-known upper bounds by Chung and...

Hadamard matrix | Graph Ramsey number | Multipartite graph | Bipartite graph | Strongly regular graph | MATHEMATICS | SET | LOWER BOUNDS

Hadamard matrix | Graph Ramsey number | Multipartite graph | Bipartite graph | Strongly regular graph | MATHEMATICS | SET | LOWER BOUNDS

Journal Article

Linear Algebra and Its Applications, ISSN 0024-3795, 07/2015, Volume 477, pp. 102 - 111

From the parameters of a directed strongly regular graph (dsrg) A. Duval (1988) showed how to compute the eigenvalues and multiplicities of the adjacency...

Rank of matrix | Directed strongly regular graph | MATHEMATICS | MATHEMATICS, APPLIED

Rank of matrix | Directed strongly regular graph | MATHEMATICS | MATHEMATICS, APPLIED

Journal Article

IEEE Transactions on Information Theory, ISSN 0018-9448, 01/2019, Volume 65, Issue 1, pp. 676 - 684

A p -ary function f...

p -ary bent function">p -ary bent function | (amorphic) association scheme | Boolean functions | strongly regular graph | Transforms | Eigenvalues and eigenfunctions | Cryptography | Indexes | Zinc | Information theory | p-ary bent function | COMPUTER SCIENCE, INFORMATION SYSTEMS | 2-WEIGHT | ENGINEERING, ELECTRICAL & ELECTRONIC

p -ary bent function">

Journal Article

Discrete Applied Mathematics, ISSN 0166-218X, 12/2014, Volume 178, pp. 153 - 156

In this note we obtain an explicit formula for the Hosoya polynomial of any distance-regular graph in terms of its intersection array. As a consequence, we...

Distance-regular graphs | Wiener index | Hosoya polynomial | Strongly regular graphs | MATHEMATICS, APPLIED | TREES

Distance-regular graphs | Wiener index | Hosoya polynomial | Strongly regular graphs | MATHEMATICS, APPLIED | TREES

Journal Article

Graphs and Combinatorics, ISSN 0911-0119, 1/2017, Volume 33, Issue 1, pp. 171 - 179

Duval, in (J Comb Theory Ser 47:71–100, 1988), introduced the concept of directed strongly regular graphs. In this paper we construct rich families of directed...

Mathematics | Engineering Design | Directed strongly regular graph | Combinatorics | Explicit construction | MATHEMATICS | DESIGNS | Graphs | Combinatorial analysis | Parameters

Mathematics | Engineering Design | Directed strongly regular graph | Combinatorics | Explicit construction | MATHEMATICS | DESIGNS | Graphs | Combinatorial analysis | Parameters

Journal Article

Journal of Algebra, ISSN 0021-8693, 01/2015, Volume 421, pp. 260 - 267

Let be an edge-regular graph with given parameters . We show how to apply a certain “block intersection polynomial” in two variables to determine a good upper...

Regular clique | Delsarte bound | Partial geometry | Orbital graph | Maximum clique | Hoffman bound | Clique | Edge-regular graph | Strongly regular graph | Quasiregular clique | MATHEMATICS

Regular clique | Delsarte bound | Partial geometry | Orbital graph | Maximum clique | Hoffman bound | Clique | Edge-regular graph | Strongly regular graph | Quasiregular clique | MATHEMATICS

Journal Article

Journal of Combinatorial Theory, Series A, ISSN 0097-3165, 01/2019, Volume 161, pp. 508 - 536

The concept of directed strongly regular graphs (DSRG) was introduced by Duval in 1988 . In the present paper, we use representation theory of finite groups in...

Induced representation | Representation theory | Directed strongly regular graph | Cayley graph | MATHEMATICS

Induced representation | Representation theory | Directed strongly regular graph | Cayley graph | MATHEMATICS

Journal Article

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