{0,1}-Brauer Configuration Algebras and Their Applications in Graph Energy Theory

Natalia Agudelo Muñetón, Agustín Moreno Cañadas, Pedro Fernando Fernández Espinosa and Isaías David Marín Gaviria
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Natalia Agudelo Muñetón: Departamento de Matemáticas, Universidad Nacional de Colombia, Edificio Yu Takeuchi 404, Kra 30 No 45-03, Bogotá 11001000, Colombia
Agustín Moreno Cañadas: Departamento de Matemáticas, Universidad Nacional de Colombia, Edificio Yu Takeuchi 404, Kra 30 No 45-03, Bogotá 11001000, Colombia
Pedro Fernando Fernández Espinosa: Departamento de Matemáticas, Universidad Nacional de Colombia, Edificio Yu Takeuchi 404, Kra 30 No 45-03, Bogotá 11001000, Colombia
Isaías David Marín Gaviria: Departamento de Matemáticas, Universidad Nacional de Colombia, Edificio Yu Takeuchi 404, Kra 30 No 45-03, Bogotá 11001000, Colombia

Mathematics, 2021, vol. 9, issue 23, 1-18

Abstract: The energy E ( G ) of a graph G is the sum of the absolute values of its adjacency matrix. In contrast, the trace norm of a digraph Q , which is the sum of the singular values of the corresponding adjacency matrix, is the oriented version of the energy of a graph. It is worth pointing out that one of the main problems in this theory consists of determining appropriated bounds of these types of energies for significant classes of graphs, digraphs and matrices, provided that, in general, finding out their exact values is a problem of great difficulty. In this paper, the trace norm of a { 0 , 1 } -Brauer configuration is introduced. It is estimated and computed by associating suitable families of graphs and posets to Brauer configuration algebras.

Keywords: brauer configuration algebra; graph energy; path algebra; poset; spectral radius; trace norm; wild representation type (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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