Name
Abstract | ||
|---|---|---|
The eccentricity matrix E(G) of a graph G is derived from the distance matrix by keeping for each row and each column only the eccentricities. The E-eigenvalues of a graph G are those of its eccentricity matrix E(G), and the eccentricity energy (or the E-energy) of G is the sum of the absolute values of E-eigenvalues. A graph is called self-centered graph if its diameter and radius are equal. In this paper, we investigate the relation between the E-energy and the ordinary energy, and we determine the exact values of E-energies of paths, cycles and double stars. Moreover, when G is an r-antipodal graph, we show that the E-energy of strong product of graphs G and H only depends on the structure of G. We finally provide upper and lower bounds for the E-energy whose extreme graphs are kinds of self-centered graphs, and we propose some potential topics for further study. |
Year | DOI | Venue |
|---|---|---|
2019 | 10.1016/j.disc.2019.05.033 | Discrete Mathematics |
Keywords | Field | DocType |
Distance,Eccentricity matrix,Energy,Self-centered graph,Antipodal graph | Discrete mathematics,Combinatorics,Strong product of graphs,Graph energy,Matrix (mathematics),Upper and lower bounds,Eccentricity (behavior),Distance matrix,Antipodal point,Eigenvalues and eigenvectors,Mathematics | Journal |
Volume | Issue | ISSN |
342 | 9 | 0012-365X |
Citations | PageRank | References |
0 | 0.34 | 0 |
Authors | ||
4 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Wang Jianfeng | 1 | 213 | 33.78 |
| Lu Lu | 2 | 3 | 3.13 |
| Milan Randić | 3 | 39 | 4.79 |
| Guo-Zheng Li | 4 | 368 | 42.62 |