Quasi-centers and radius related to some iterated line digraphs, proofs of several conjectures on de Bruijn and Kautz graphs

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• 作者：Nicolas Lichiardopol ^{nicolas.lichiardopol@neuf.fr" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Quasi-center ; Radius ; Walk ; de Bruijn graph ; Kautz graph
• 刊名：Discrete Applied Mathematics
• 出版年：2016
• 出版时间：31 March 2016
• 年：2016
• 卷：202
• 期：Complete
• 页码：106-110
• 全文大小：371 K

文摘

Bond (1987) and Bond et al. (1987), conjectured that a quasi-center in an undirected de Bruijn graph UB(d,D)$UB(d,D)$ has cardinality at least d−1$d-1$, and that a quasi-center in an undirected Kautz graph UK(d,D)$UK(d,D)$ has cardinality at least d$d$. They proved that for d≥3$d\ge 3$, the radii of UB(d,D)$UB(d,D)$ and UK(d,D)$UK(d,D)$ are both equals to a223da63e7fcbfaf470d1eb18baa" title="Click to view the MathML source">D$D$, and conjectured also that the radii of 16a2672879" title="Click to view the MathML source">UB(2,D)$UB(2,D)$ and UK(2,D)$UK(2,D)$ are respectively D−1$D-1$ and a223da63e7fcbfaf470d1eb18baa" title="Click to view the MathML source">D$D$. In this paper we give results in a more general context which validate these conjectures (excepting that asserting that the radius of 16a2672879" title="Click to view the MathML source">UB(2,D)$UB(2,D)$ is D−1$D-1$), and give simplified proofs of the cited results.