Some properties of graphs constructed from 2-designs

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• 作者：Xu Yang^a ; ^{xcubicy@163.com" class="auth_mail" title="E-mail the corresponding author} ; Lihua Feng^a ; ^{fenglh@163.com" class="auth_mail" title="E-mail the corresponding author} ; Weijun Liu ; ^a ; ^b ; ^{wjliu6210@126.com" class="auth_mail" title="E-mail the corresponding author} ; ^{wjliu@csu.edu.cnv" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Design ; Bipartite graph ; Semisymmetric graph ; Flag-transitive
• 刊名：Applied Mathematics and Computation
• 出版年：2016
• 出版时间：5 July 2016
• 年：2016
• 卷：284
• 期：Complete
• 页码：1-11
• 全文大小：502 K

文摘

Let D=(P,B)$\mathbb{D}=(\mathbb{P},\mathbb{B})$ be any nontrivial nonsymmetric 2-(v, k, λ  ) design. In this paper we construct a connected, regular and bipartite graph, say IG_v,b(D),${\mathsf{IG}}_{v,b}\left(\mathbb{D}\right),$ from D$\mathbb{D}$. Some graphic properties of IG_v,b(D)${\mathsf{IG}}_{v,b}\left(\mathbb{D}\right)$ are investigated. In particular, the results in the paper bridges the equivalency between edge-transitivity of IG_v,b(D)${\mathsf{IG}}_{v,b}\left(\mathbb{D}\right)$ and flag-transitivity of D$\mathbb{D}$. With the equivalency, it is obtained that IG_v,b(D)${\mathsf{IG}}_{v,b}\left(\mathbb{D}\right)$ is a semisymmetric graph as long as D$\mathbb{D}$ is a nonsymmetric flag-transitive 2-(v, k, λ) design.