I'm having difficulty understanding a fact stated in a research paper I'm reading. Namely, let $T$ be a tree with all nodes of degree $4$ (ie, the root has $4$ daughter nodes and all other nodes have $3$ daughter nodes). The paper states without explanation that the spectrum of the Laplacian on $T$ is in $[4-2\sqrt{3},\infty)$.


How does one derive this result? I've searched around but haven't found many resources addressing this particular topic.



Spectrum of Laplacian matrix of an infinite tree graph
A very lucid explanation is given in [Luca Trevisan's blog.](https://lucatrevisan.wordpress.com/2014/08/20/the-spectrum-of-the-infinite-tree/)


