Spectra of graphs and the spectral criterion for property (T)
نویسنده
چکیده
For a finite connected graph X , we consider the graph RX obtained from X by associating a new vertex to every edge of X and joining by edges the extremities of each edge of X to the corresponding new vertex. We express the spectrum of the Laplace operator on RX as a function of the corresponding spectrum on X . As a corollary, we show that X is a complete graph if and only if λ1(RX) > 1 2 . We give a re-interpretation of the correspondence X 7→ RX in terms of the right-angled Coxeter group defined by X .
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عنوان ژورنال:
- EJGTA
دوره 5 شماره
صفحات -
تاریخ انتشار 2017