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Description: |
Let D be a digraph, its energy is defined as the sum of the absolutes values of the real parts of the eigenvalues of its adjacency matrix A(D). This concept was introduced by J. Rada in 2008 as a generalization of the concept of graph energy introduced by I. Gutman in 1978. The concept of graph energy arose in chemistry where it is used to aproximate the total pi-electron energy of non-saturated hydrocarbons, taking a graph G as a representation of the molecule. In this seminar we will present some resent results of a joint work with J. Rada, about an upper bound for the spectral radius of a digraph in terms of its vertices and closed walks of length 2. As an application of this result, we construct new sharp upper bounds for the energy of a digraph.
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