Strongly regular graphs satisfying the 4-vertex condition

Brouwer, Andries E.; Ihringer, Ferdinand; Kantor, William M.

doi:10.48550/arxiv.2107.00076

Cited by 2 publications

(9 citation statements)

References 25 publications

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“…If q = 3 and d = 2, then, by Theorem 1, we have parameters (36,24,15,16,4,9). By Theorem 2, from any divisible design graph with parameters (36,24,15,16,4,9) and a 2-(4, 3, 2) design we can construct a strongly regular graph with parameters (40,27,18,18). The complement of this graph has parameters (40, 12,2,4).…”

Section: Examples With Small Number Of Verticesmentioning

confidence: 98%

“…If q = 2 and d = 2, then, by Theorem 1, a divisible design graph has parameters (12,6,2,3,3,4). The line graph of the octahedron is a unique graph with such parameters.…”

Section: Examples With Small Number Of Verticesmentioning

confidence: 99%

“…By Theorem 2, we have the triangular graph T (6) which is a strongly regular graph with parameters (15,8,4,4). D. Panasenko and L. Shalaginov [15] found all divisible design graphs up to 39 vertices by direct computer calculations, except for the three tuples of parameters: (32, 15,6,7,4,8), (32,17,8,9,4,8), (36,24,15,16,4,9). These cases turned out to be very difficult to calculate.…”

Section: Examples With Small Number Of Verticesmentioning

confidence: 99%

“…By Theorem 2, from any divisible design graph with parameters (36,24,15,16,4,9) and a 2-(4, 3, 2) design we can construct a strongly regular graph with parameters (40,27,18,18). The complement of this graph has parameters (40, 12,2,4). All strongly regular graphs with parameters (40, 12, 2, 4) were found by E. Spence [16].…”

Section: Examples With Small Number Of Verticesmentioning

confidence: 99%

“…Brouwer, Email address: vvk@imm.uran.ru (Vladislav V. Kabanov) F. Ihringer and W.M. Kantor [4] described a switching operation on collinearity graphs of polar spaces to obtain graphs that satisfy the 4-vertex condition if the original graph belongs to a symplectic polar space.…”

Section: Introductionmentioning

confidence: 99%

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A new construction of strongly regular graphs with parameters of the complement symplectic graph

Kabanov¹

2022

Preprint

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Symplectic graph Sp(2d, q) is the collinearity graph of the symplectic space of dimension 2d over a finite field of order q. A k-regular graph on v vertices is a divisible design graph with parameters (v, k, λ 1 , λ 2 , m, n) if its vertex set can be partitioned into m classes of size n, such that any two different vertices from the same class have λ 1 common neighbours, and any two vertices from different classes have λ 2 common neighbours whenever it is not complete or edgeless. In this paper we present a new prolific construction of strongly regular graphs with parameters of the complement of symplectic graphs using a new prolific construction of one type of divisible design graphs.

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Section: Examples With Small Number Of Verticesmentioning

confidence: 98%

“…If q = 2 and d = 2, then, by Theorem 1, a divisible design graph has parameters (12,6,2,3,3,4). The line graph of the octahedron is a unique graph with such parameters.…”

Section: Examples With Small Number Of Verticesmentioning

confidence: 99%

Section: Examples With Small Number Of Verticesmentioning

confidence: 99%

Section: Examples With Small Number Of Verticesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

A new construction of strongly regular graphs with parameters of the complement symplectic graph

Kabanov¹

2022

Preprint

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A New Construction of Strongly Regular Graphs with Parameters of the Complement Symplectic Graph

Kabanov

2023

Electron. J. Combin.

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The symplectic graph $Sp(2d, q)$ is the collinearity graph of the symplectic space of dimension $2d$ over the finite field of order $q$. A $k$-regular graph on $v$ vertices is a divisible design graph with parameters $(v,k,\lambda_1,\lambda_2,m,n)$ if its vertex set can be partitioned into $m$ classes of size $n$, such that any two different vertices from the same class have $\lambda_1$ common neighbours, and any two vertices from different classes have $\lambda_2$ common neighbours whenever it is not complete or edgeless. In this paper we propose a new construction of strongly regular graphs with the parameters of the complement of the symplectic graph using divisible design graphs.

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Strongly regular graphs satisfying the 4-vertex condition

Cited by 2 publications

References 25 publications

A new construction of strongly regular graphs with parameters of the complement symplectic graph

A new construction of strongly regular graphs with parameters of the complement symplectic graph

A New Construction of Strongly Regular Graphs with Parameters of the Complement Symplectic Graph

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