On λ_1-extremal non-regular graphs
On λ_1-extremal non-regular graphs
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DOI：
10.13001/1081-3810.1341
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发表时间：
2009
影响因子：
0.7
通讯作者：
Bolian Liu;Yufei Huang;Zhifu You
中科院分区：
文献类型：
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作者：
Bolian Liu;Yufei Huang;Zhifu You
设G是一个有n个顶点，最大度数∆，最小度数δ的连通非正则图，设λ1为G.I邻接矩阵的最大特征值。本文通过研究G的Perron向量，证明了i -a型图和i -b型图(分别为：具有某些特定性质的type-II-a)图不是λ1极值图。并且，对于每一个连通的非正则图，都得到了∆与λ1之差的下界。
Let G be a connected non-regular graph with n vertices, maximum degree ∆ and minimum degree δ ,a nd letλ1 be the greatest eigenvalue of the adjacency matrix of G.I n this paper, by studying the Perron vector of G, it is shown that type-I-a graphs and type-I-b (resp. type-II-a) graphs with some specified properties are not λ1-extremal graphs. Moreover, for each connected non-regular graph some lower bounds on the difference between ∆ and λ1 are obtained.