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math.SP2026
-sectorial discrete Laplacians and recurrence of complex-weighted graphs
Anna Muranova
We consider complex-weighted graphs, whose edge weights belong to a sector in the complex plane. We show that the corresponding Dirichlet Laplacian is -sectorial, and, hence, ge…
math.SP2026
Periodic discrete graphs with prescribed spectrum
Andrii Khrabustovskyi, Anna Muranova
We construct a periodic weighted graph whose discrete Laplacian has a spectrum with precisely gaps. Moreover, we show that by an appropriate choice of the weights, the endpoint…
math.AT2026
Burnings of trees and their homologies
Yuri Muranov, Anna Muranova
The problem of graph burning was firstly introduced as a model for different processes of social and network interactions. Recently, the authors of the present paper developed meth…