Connected graphs with maximal Q-index: The one-dominating-vertex case |
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Authors: | Ting-Chung Chang |
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Affiliation: | a Chihlee Institute of Technology, New Taipei City 22050, Taiwan, ROC b Department of Mathematics, Tamkang University, New Taipei City 25137, Taiwan, ROC |
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Abstract: | By the signless Laplacian of a (simple) graph G we mean the matrix Q(G)=D(G)+A(G), where A(G),D(G) denote respectively the adjacency matrix and the diagonal matrix of vertex degrees of G. For every pair of positive integers n,k, it is proved that if 3?k?n-3, then Hn,k, the graph obtained from the star K1,n-1 by joining a vertex of degree 1 to k+1 other vertices of degree 1, is the unique connected graph that maximizes the largest signless Laplacian eigenvalue over all connected graphs with n vertices and n+k edges. |
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Keywords: | 05C07 05C35 05C50 15A18 |
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