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On the distance signless Laplacian spectral radius of graphs

✍ Scribed by Xing, Rundan; Zhou, Bo; Li, Jianping

Book ID
125503704
Publisher
Taylor and Francis Group
Year
2013
Tongue
English
Weight
157 KB
Volume
62
Category
Article
ISSN
0308-1087

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By the signless Laplacian of a (simple) graph G we mean the matrix , where A(G), D(G) denote respectively the adjacency matrix and the diagonal matrix of vertex degrees of G. It is known that connected graphs G that maximize the signless Laplacian spectral radius ρ(Q (G)) over all connected graphs

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In this paper, we show that among all the connected graphs with n vertices and k cut vertices, the maximal signless Laplacian spectral radius is attained uniquely at the graph G n,k , where G n,k is obtained from the complete graph K n-k by attaching paths of almost equal lengths to all vertices of