Weighted spectra on a weighted geometric realization of 2-simplexes and 3-simplexes
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Published:2022-08-27
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Volume:
Page:
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ISSN:1793-8309
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Container-title:Discrete Mathematics, Algorithms and Applications
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language:en
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Short-container-title:Discrete Math. Algorithm. Appl.
Author:
Baalal Azeddine1,
Hatim Khalid1
Affiliation:
1. Fundamental and Applied Mathematics Laboratory, Department of Mathematics and Computer Science, Faculty of Sciences Aïn Chock, Hassan II University of Casablanca, Morocco
Abstract
In this paper, we construct a weighted geometric realization of the set of [Formula: see text]-simplexes and [Formula: see text]-simplexes. On this weighted geometric realization, we create the Laplacian associated to [Formula: see text]-simplexes [Formula: see text] and the Laplacian associated to [Formula: see text]-simplexes [Formula: see text]. We prove that the nonzero spectrum of [Formula: see text] is the same as the nonzero spectrum of [Formula: see text]. For [Formula: see text], we show that [Formula: see text] belongs to the spectrum of [Formula: see text] or to the spectrum of [Formula: see text].
Publisher
World Scientific Pub Co Pte Ltd
Subject
Discrete Mathematics and Combinatorics