3-bounded property in a triangle-free distance-regular graph

Pan, Yeh-Jong; Weng, Chih-wen

doi:10.1016/j.ejc.2007.10.002

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Introduction1

The Shape Of Pentagons1

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2009

2024

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Cited by 3 publications

(2 citation statements)

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“…The proof of Theorem 5 is given in Section 4. Theorem 5 is a generalization of [2,Lemma 4.3.13] and [7]. Combining Theorem 4 and Theorem 5, we have the (ii) ⇒ (i) part of the following theorem.…”

Section: Introductionmentioning

confidence: 65%

See 1 more Smart Citation

Nonexistence of a Class of Distance-Regular Graphs

Huang¹,

Pan²,

Weng³

2015

Electron. J. Combin.

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Let $\Gamma$ denote a distance-regular graph with diameter $D \geq 3$ and intersection numbers $a_1=0, a_2 \neq 0$, and $c_2=1$. We show a connection between the $d$-bounded property and the nonexistence of parallelograms of any length up to $d+1$. Assume further that $\Gamma$ is with classical parameters $(D, b, \alpha, \beta)$, Pan and Weng (2009) showed that $(b, \alpha, \beta)= (-2, -2, ((-2)^{D+1}-1)/3).$ Under the assumption $D \geq 4$, we exclude this class of graphs by an application of the above connection.

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Section: Introductionmentioning

confidence: 65%

“…Throughout this section, let Γ = (X, R) denote a distance-regular graph with diameter D 3, and intersection numbers a 1 = 0, a 2 = 0. Such graphs are also studied in [4,5,6,7,8].…”

Section: The Shape Of Pentagonsmentioning

confidence: 99%