| Journal: | Proyecciones (Antofagasta) |
| Database: | PERIÓDICA |
| System number: | 000406121 |
| ISSN: | 0716-0917 |
| Authors: | Monsalve, Juan1 Rada, Juan1 |
| Institutions: | 1Universidad de Antioquia, Instituto de Matemáticas, Medellín, Antioquia. Colombia |
| Year: | 2016 |
| Season: | Dic |
| Volumen: | 35 |
| Number: | 4 |
| Pages: | 395-404 |
| Country: | Chile |
| Language: | Inglés |
| Document type: | Artículo |
| Approach: | Analítico |
| English abstract | The energy of a digraph is defined as E (D) = Pn k=1 |Re (zk)|, where z1,...,zn are the eigenvalues of the adjacency matrix of D. This is a generalization of the concept of energy introduced by I. Gutman in 1978 [3]. When the characteristic polynomial of a digraph D is of the form φD (z) = b n X2 c k=0 (−1)k bk (D) zn−2k (0.1) where b0 (D)=1 and bk (D) ≥ 0 for all k, we show that E (D) = 2 π Z∞ 0 1 t2 ln ⎡ ⎢ ⎣ b n X2 c k=0 bk (D)t 2k ⎤ ⎥ (0.2) ⎦ dt 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) |
| Disciplines: | Matemáticas |
| Keyword: | Matemáticas aplicadas, Matemáticas puras, Combinatoria, Teoría de gráficas, Algebra lineal, Digrafos, Ciclos |
| Keyword: | Mathematics, Applied mathematics, Pure mathematics, Combinatorics, Graph theory, Linear algebra, Digraphs, Cycles |
| Full text: | Texto completo (Ver PDF) |
