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

Mathematics

Agustín Moreno Cañadas¹  Pedro Fernando Fernández Espinosa¹  Isaías David Marín Gaviria¹  Natalia Agudelo Muñetón¹ 

[1] Departamento de Matemáticas, Universidad Nacional de Colombia, Edificio Yu Takeuchi 404, Kra 30 No 45-03, Bogotá 11001000, Colombia;

关键词: brauer configuration algebra;    graph energy;    path algebra;    poset;    spectral radius;    trace norm;   

DOI  :  10.3390/math9233042

来源: DOAJ

【 摘 要 】

The energy $\mathcal{E}\left(G\right)$ 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.

【 授权许可】

Unknown