Eccentricity energy change of complete multipartite graphs due to edge deletion

被引:13
作者
Mahato, Iswar [1 ]
Kannan, M. Rajesh [1 ]
机构
[1] Indian Inst Technol Kharagpur, Dept Math, Kharagpur 721302, W Bengal, India
来源
SPECIAL MATRICES | 2022年 / 10卷 / 01期
关键词
Complete multipartite graph; Eccentricity matrix; Eccentricity energy; DISTANCE ENERGY; MATRIX; SPECTRA;
D O I
10.1515/spma-2021-0156
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
The eccentricity matrix epsilon(G) of a graph G is obtained from the distance matrix of G by retaining the largest distances in each row and each column, and leaving zeros in the remaining ones. The eccentricity energy of G is sum of the absolute values of the eigenvalues of epsilon(G). Although the eccentricity matrices of graphs are closely related to the distance matrices of graphs, a number of properties of eccentricity matrices are substantially different from those of the distance matrices. The change in eccentricity energy of a graph due to an edge deletion is one such property. In this article, we give examples of graphs for which the eccentricity energy increase (resp., decrease) but the distance energy decrease (resp., increase) due to an edge deletion. Also, we prove that the eccentricity energy of the complete k-partite graph k(n1,...,nk) with k >= 2 and n(i) >= 2, increases due to an edge deletion.
引用
收藏
页码:193 / 202
页数:10
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