On quasi-strongly regular graphs with parameters <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e60" altimg="si11.svg"><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>a</mml:mi><mml:mo>;</mml:mo><mml:mi>k</mml:mi><mml:mo linebreak="goodbreak" linebreakstyle="after">−</mml:mo><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:msub><mml:mrow><mml:mi>c</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mo

Xie, Jiayi; Jia, Dongdong; Zhang, Gengsheng

doi:10.1016/j.disc.2020.112237

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“…Moreover, we can characterize these graphs whose n is equal to the upper or lower bound. Some proper quasi-strongly regular graphs with particular parameters have been characterized in [13,22]. According to our knowledge, these graphs of grade higher than 2 with any parameters have not been characterized yet.…”

Section: Introductionmentioning

confidence: 99%

Quasi-strongly regular graphs of grade three with diameter two

Sriwongsa,

Kaemawichanurat

2021

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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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Section: Introductionmentioning

confidence: 99%