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拉普拉斯整谱三圈图的刻画
引用本文:景维龙,文飞,黄琼湘.拉普拉斯整谱三圈图的刻画[J].新疆大学学报(理工版),2014(1):26-32.
作者姓名:景维龙  文飞  黄琼湘
作者单位:新疆大学数学与系统科学学院,新疆乌鲁木齐830046
基金项目:This work is supported by NSFC Grant No(11261059).
摘    要:如果一个图的拉普拉斯谱都是由整数构成的,那么这个图称为拉普拉斯整谱图。本文首先刻画了拉普拉斯三圈基图中最长圈的圈长c(H)≤6的整谱图,并且找出这些连通的拉普拉斯三圈基图的整谱图;其次刻画了至少含有一个悬挂点的连通三圈图的拉普拉斯整谱图,最后证明了至少含有一个悬挂点的连通三圈图的拉普拉斯整谱图都是由它们的拉普拉斯谱唯一确定的。

关 键 词:拉普拉斯整图  拉普拉斯谱  三圈基图  三圈图

On the Laplacian Integral of Tricyclic Graphs
JING Wei-long,WEN Fei,HUANG Qiong-xiang.On the Laplacian Integral of Tricyclic Graphs[J].Journal of Xinjiang University(Science & Engineering),2014(1):26-32.
Authors:JING Wei-long  WEN Fei  HUANG Qiong-xiang
Institution:(College of Mathematics and System Sciences, Xinjiang University, Urumqi, Xinjiang 830046, China)
Abstract:A graph is a Laplacian integral graph if the Laplacian spectrum consists of integers. In this paper, we find all the Laplacian integer tricyclic base-graphs H with c(H)≤6 where c(H) is the circumference of H. Next we show all the Laplacian integer tricyclic graphs of order n with at least one pendent. Moreover, we show that all the Laplacian integer tricyclic graphs of order n with at least one pendent are determined by their Laplacian spectra.
Keywords:Laplacian integral graph  Laplacian spectrum  tricyclic base-graph  tricyclic graph
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