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arXiv · 1703.01839

The spectral radius of graphs with no $K_{2,t}$ minor

V. Nikiforov
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Abstract

Let $t\geq3$ and $G$ be a graph of order $n,$ with no $K_{2,t}$ minor. If $n>400t^{6}$, then the spectral radius $μ\left( G\right) $ satisfies \[ μ\left( G\right) \leq\frac{t-1}{2}+\sqrt{n+\frac{t^{2}-2t-3}{4}}, \] with equality if and only if $n\equiv1$ $(\operatorname{mod}$ $t)$ and $G=K_{1}\vee\left\lfloor n/t\right\rfloor K_{t}$. For $t=3$ the maximum $μ\left( G\right) $ is found exactly for any $n>40000$.

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V. Nikiforov. 2017-03-06. The spectral radius of graphs with no $K_{2,t}$ minor. https://arxiv.org/abs/1703.01839

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