Graph energy based on the eccentricity matrix
Graph energy based on the eccentricity matrix
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DOI：
10.1016/j.disc.2019.05.033
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发表时间：
2019-09
期刊：
影响因子：
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通讯作者：
Jianfeng Wang;Lu Lu-Lu;M. Randic;Guozheng Li
中科院分区：
文献类型：
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作者：
Jianfeng Wang;Lu Lu-Lu;M. Randic;Guozheng Li
图G的偏心矩阵E(G)是由距离矩阵导出的，它只保留每行和每列的偏心率。图G的E-特征值是它的偏心矩阵E(G)的E-特征值，G的偏心能量(或E-能量)是E-特征值的绝对值之和。如果一个图的直径和半径相等，则称它为自中心图。本文研究了E能量与普通能量的关系，确定了路径、周期和双星的E能量的精确值。此外，当G是r-对偶图时，我们证明了图G和图H的强积的E-能量仅取决于G的结构。最后，我们给出了极图为自中心图的E-能量的上界和下界，并提出了一些潜在的研究方向。
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.