Abstract
ABSTRACT In this paper, we prove that if G is a -minor free graph of order with , the signless Laplacian spectral radius with equality if and only if and , where for n − s + 1=pt + r and . In particular, if t=3 and , then is the unique -minor free graph of order n with the maximum signless Laplacian spectral radius. In addition, is the unique extremal graph with the maximum signless Laplacian spectral radius among all -minor free graphs of order .
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