On strictly Deza graphs with parameters <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="mml1" display="inline" overflow="scroll" altimg="si1.gif"><mml:mrow><mml:mo>(</mml:mo><mml:mi>n</mml:mi><mml:mo>,</mml:mo><mml:mi>k</mml:mi><mml:mo>,</mml:mo><mml:mi>k</mml:mi><mml:mo>−</mml:mo><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mi>a</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math>

Kabanov, V. V.; Maslova, N. V.; Shalaginov, Leonid

doi:10.1016/j.ejc.2018.07.011

Cited by 8 publications

(3 citation statements)

References 13 publications

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“…Let ∆ be a strictly Deza graph with parameters (n, k, k − 1, a). In the case β > 1, ∆ is shown to be the lexicographical product of a complete multipartite graph with parts of the same size and an edge (see [27,Theorem]). In the case β = 1, ∆ can be constructed from a strongly regular graph with parameters λ − µ = −1 with use of certain two operations: the lexicographical product with an edge and, possibly, dual Seidel switching (see [15,Theorem 2]).…”

Section: Characterisations Of Deza Graphs With Special Parametersmentioning

confidence: 99%

Deza graphs: a survey and new results

Goryaĭnov¹,

Shalaginov²

2021

Preprint

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In this paper we survey existing results on Deza graphs and give some new results. We present an introduction to Deza graphs for the reader who is unfamiliar with the subject, and then give an overview of some developments in the area of Deza graphs since the initial paper by five authors [M. Erickson, S. Fernando, W. H. Haemers, D. Hardy, J. Hemmeter, Deza graphs: A generalization of strongly regular graphs, J. Comb. Designs. 7 (1999), 395-405.] was written. We then investigate 3-class cyclotomic schemes and give necessary and sufficient conditions to get a Deza graph as a graph given by one relation or the union of two relations. Finally, we prove that a strictly Deza circulant on 2p vertices, where p is prime, is isomorphic to the lexicographical product of the Paley graph on p vertices with an edge.

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Section: Characterisations Of Deza Graphs With Special Parametersmentioning

confidence: 99%

Deza graphs: a survey and new results

Goryaĭnov¹,

Shalaginov²

2021

Preprint

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“…These three constructions were considered in two papers [4,9] on Deza graphs with parameters (v, k, k − 1, a).…”

Section: Let M Be the Adjacency Matrix Of γ And P Be A Non-identity P...mentioning

confidence: 99%

Enumeration of strictly Deza graphs with at most 21 vertices

Goryainov,

Panasenko,

Shalaginov

2021

Preprint

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“…In fact the authors were inspired by Deza and Deza [5] who provided relationship of some Deza graph in their work concerning metric polytope. For more example of studies in Deza graphs see [12,15,16]. Another generalization of strongly regular graphs is the concept of quasi-strongly regular graphs which was introduced in Golightly et.…”

Section: Introductionmentioning

confidence: 99%

Quasi-strongly regular graphs of grade three with diameter two

Sriwongsa,

Kaemawichanurat

2021

Preprint

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A quasi-strongly regular graph of grade p with parameters (n, k, a; c 1 , . . . , cp) is a k-regular graph of order n such that any two adjacent vertices share a common neighbours and any two non-adjacent vertices share c i common neighbours for some 1 ≤ i ≤ p. This is a generalization of a strongly regular graph. In this paper, we focus on strictly quasi-strongly regular graphs of grade 3 with c i = k − i for i = 1, 2, 3. The main result is to show the sharp bounds of order n for a given k ≥ 4. Furthermore, by this result, we characterize all of these graphs whose n satisfies upper or lower bounds.

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On strictly Deza graphs with parameters (n,k,k−1,a)

Cited by 8 publications

References 13 publications

Deza graphs: a survey and new results

Deza graphs: a survey and new results

Enumeration of strictly Deza graphs with at most 21 vertices

Quasi-strongly regular graphs of grade three with diameter two

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