Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5775706 | Applied Mathematics and Computation | 2017 | 9 Pages |
Abstract
Let Mn(C) denote the space of n à n matrices with entries in C. We define the energy of AâMn(C) as
(1)E(A)=âk=1n|λkâtr(A)n|where λ1,â¦,λn are the eigenvalues of A, tr(A) is the trace of A and |z| denotes the modulus of zâC. If A is the adjacency matrix of a graph G then E(A) is precisely the energy of the graph G introduced by Gutman in 1978. In this paper, we compare the energy E with other well-known energies defined over matrices. Then we find upper and lower bounds of E which extend well-known results for the energies of graphs and digraphs. Also, we obtain new results on energies defined over the adjacency, Laplacian and signless Laplacian matrices of digraphs.
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Diego Bravo, Florencia CubrÃa, Juan Rada,