Energy of strongly connected digraphs whose underlying graph is a cycle
The energy of a digraph is defined as E (D) =∑1n|Re (z k)|, where z1,..., z n are the eigenvalues of the adjacency matrix of D. This is a generalization of the concept of energy introduced by I. Gutman in 1978. When the characteristic polynomial ofa digraph D is ofthe form <img width=38...
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| Autores principales: | , |
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| Lenguaje: | English |
| Publicado: |
Universidad Católica del Norte, Departamento de Matemáticas
2016
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| Materias: | |
| Acceso en línea: | http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172016000400003 |
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| Sumario: | The energy of a digraph is defined as E (D) =∑1n|Re (z k)|, where z1,..., z n are the eigenvalues of the adjacency matrix of D. This is a generalization of the concept of energy introduced by I. Gutman in 1978. When the characteristic polynomial ofa digraph D is ofthe form <img width=387 height=66 src="../../../../../Users/Raul%20Jimenez/Desktop/F01art01.jpg"> where bo (D) = 1 and b k(D) ≥ 0 for all k, we show that <img src="../imagenes/F02art01.jpg" alt="" width="385" height="72"> This expression for the energy has many applications in the study of extremal values of the energy in special classes of digraphs. In this paper we consider the set D* (Cn) of all strongly connected digraphs whose underlying graph is the cycle Cn, and characterize those whose characteristic polynomial is of the form (0.1). As a consequence, we find the extremal values of the energy based on (0.2). |
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