The changes in distance Laplacian spectral radius of graphs resulting from graft transformations

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• 作者：Hongying Lin ^{lhongying0908@126.com} ; Bo Zhou ; ^{zhoubo@scnu.edu.cn}
• 关键词：Distance Laplacian spectral radius ; Distance Laplacian matrix ; Graft transformation ; Non-starlike tree ; Non-caterpillar tree ; Clique number
• 刊名：Discrete Applied Mathematics
• 出版年：2017
• 出版时间：11 March 2017
• 年：2017
• 卷：219
• 期：Complete
• 页码：147-157
• 全文大小：465 K
• 卷排序：219

文摘

For a connected graph GG, the distance Laplacian spectral radius of GG is the spectral radius of its distance Laplacian matrix L(G)L(G) defined as L(G)=Tr(G)−D(G)L(G)=Tr(G)−D(G), where Tr(G)Tr(G) is a diagonal matrix of vertex transmissions of GG and D(G)D(G) is the distance matrix of GG. In this paper, we study the change in the distance Laplacian spectral radius of graphs by some graft transformations, and as applications, we determine the unique graphs with minimum distance Laplacian spectral radius among non-caterpillar trees, and among non-starlike non-caterpillar trees, respectively, we prove that the path is the unique graph with maximum distance Laplacian spectral radius among connected graphs, and determine the unique graph with maximum distance Laplacian spectral radius among connected graphs with given clique number.