Name
Abstract | ||
|---|---|---|
Let Mn(C) denote the space of n × n matrices with entries in C. We define the energy of A∈Mn(C) as
(1)E(A)=∑k=1n|λk−tr(A)n|where λ1,…,λn are the eigenvalues of A, tr(A) is the trace of A and |z| denotes the modulus of z∈C. 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. |
Year | DOI | Venue |
|---|---|---|
2017 | 10.1016/j.amc.2017.05.051 | Applied Mathematics and Computation |
Keywords | DocType | Volume |
Energy of matrices,Energy of graphs | Journal | 312 |
ISSN | Citations | PageRank |
0096-3003 | 0 | 0.34 |
References | Authors | |
0 | 3 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Diego O. Bravo | 1 | 0 | 0.34 |
| Florencia Cubría | 2 | 0 | 0.34 |
| Juan Rada | 3 | 36 | 10.02 |