IJPAM: Volume 36, No. 3 (2007)

EQUIENERGETIC DIGRAPHS

Williams López$^1$, Juan Rada$^2$
$^{1,2}$Departamento de Matemáticas
Facultad de Ciencias
Universidad de Los Andes
Mérida, 5101, VENEZUELA
$^1$e-mail: wlopez@ula.ve
$^2$e-mail: juanrada@ula.ve


Abstract.The energy of a graph $G$ is defined as $\mathbb{E}\left( G\right) =\sum\limits_{i=1}^{n}\left\vert \lambda _{i}\right\vert $, where $\lambda _{1},\ldots ,\lambda _{n}$ are the eigenvalues of the adjacency matrix of $G$. Recently, many authors have considered the problem of generating pairs of non-cospectral equienergetic graphs. Since every graph $G$ can be identified with a symmetric digraph $G^{\ast }$, and the concept of the energy was recently generalized to digraphs, it is natural to consider the problem of generating pairs of non-symmetric, non-cospectral and equienergetic digraphs.

Received: January 10, 2007

AMS Subject Classification: 05C25

Key Words and Phrases: energy of a graph, eigenvalues of the adjacency matrix, non-cospectral equienergetic graphs, symmetric digraph, non-symmetric digraphs, non-cospectral digraphs, equienergetic digraphs

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2007
Volume: 36
Issue: 3