Complete split graph determined by its (signless) Laplacian spectrum

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• 作者：Kinkar Ch. Das^a ; ^{kinkardas2003@googlemail.com" class="auth_mail" title="E-mail the corresponding author} ; Muhuo Liu^b ; ^{liumuhuo@163.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Complete split graph ; Determined by graph spectrum ; (Signless) Laplacian spectrum
• 刊名：Discrete Applied Mathematics
• 出版年：2016
• 出版时间：31 May 2016
• 年：2016
• 卷：205
• 期：Complete
• 页码：45-51
• 全文大小：387 K

文摘

A complete split graph 16000044&_mathId=si1.gif&_user=111111111&_pii=S0166218X16000044&_rdoc=1&_issn=0166218X&md5=febd683cc1c57a97455d9be14ff128b6">16000044-si1.gif">$CS(n,\alpha )$, is a graph on 16000044&_mathId=si2.gif&_user=111111111&_pii=S0166218X16000044&_rdoc=1&_issn=0166218X&md5=7fc766d724d5f9eae4e72ee48c5d9316" title="Click to view the MathML source">n$n$ vertices consisting of a clique on 16000044&_mathId=si3.gif&_user=111111111&_pii=S0166218X16000044&_rdoc=1&_issn=0166218X&md5=de55232bd14c6b6843b2c487657b34be" title="Click to view the MathML source">n−α$n-\alpha$ vertices and an independent set on the remaining 16000044&_mathId=si4.gif&_user=111111111&_pii=S0166218X16000044&_rdoc=1&_issn=0166218X&md5=ddce219cb98226441669bac84304a1ea">16000044-si4.gif">$\alpha (1\le \alpha \le n-1)$ vertices in which each vertex of the clique is adjacent to each vertex of the independent set. In this paper, we prove that 16000044&_mathId=si1.gif&_user=111111111&_pii=S0166218X16000044&_rdoc=1&_issn=0166218X&md5=febd683cc1c57a97455d9be14ff128b6">16000044-si1.gif">$CS(n,\alpha )$ is determined by its Laplacian spectrum when 16000044&_mathId=si6.gif&_user=111111111&_pii=S0166218X16000044&_rdoc=1&_issn=0166218X&md5=d15e7801b1a85b20ab068252f1f7992c" title="Click to view the MathML source">1≤α≤n−1$1\le \alpha \le n-1$, and 16000044&_mathId=si1.gif&_user=111111111&_pii=S0166218X16000044&_rdoc=1&_issn=0166218X&md5=febd683cc1c57a97455d9be14ff128b6">16000044-si1.gif">$CS(n,\alpha )$ is also determined by its signless Laplacian spectrum when 16000044&_mathId=si6.gif&_user=111111111&_pii=S0166218X16000044&_rdoc=1&_issn=0166218X&md5=d15e7801b1a85b20ab068252f1f7992c" title="Click to view the MathML source">1≤α≤n−1$1\le \alpha \le n-1$ and 16000044&_mathId=si9.gif&_user=111111111&_pii=S0166218X16000044&_rdoc=1&_issn=0166218X&md5=78486213c03983091dc72256a77ba944" title="Click to view the MathML source">α≠3$\alpha \ne 3$.