Abstract
Let G be a connected graph and Q(G) be the signless Laplacian of G. The principal ratio γ(G) of Q(G) is the ratio of the maximum and minimum entries of the Perron vector of Q(G). In this paper, we consider the maximum principal ratio γ(G) among all connected graphs of order n, and show that for sufficiently large n the extremal graph is a kite graph obtained by identifying an end vertex of a path to any vertex of a complete graph.
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