On the signless Laplacian spectral radius of Ks,t-minor free graphs

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 n >= 1186.

Automated summary

This paper proves that under certain conditions, -minor free graphs have the maximum signless Laplacian spectral radius, with the absence of a specific subgraph structure. When t=3 and p=0, the graph is the unique one that satisfies the conditions for having the maximum signless Laplacian spectral radius.