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Eccentricity energy change of complete multipartite graphs due to edge deletion
- Source :
- Special Matrices, Vol 10, Iss 1, Pp 193-202 (2022)
- Publication Year :
- 2022
- Publisher :
- De Gruyter, 2022.
-
Abstract
- The eccentricity matrix ɛ(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 ɛ(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 Kn1,...,nk with k ≥ 2 and ni ≥ 2, increases due to an edge deletion.
Details
- Language :
- English
- ISSN :
- 23007451
- Volume :
- 10
- Issue :
- 1
- Database :
- Directory of Open Access Journals
- Journal :
- Special Matrices
- Publication Type :
- Academic Journal
- Accession number :
- edsdoj.304d6c0b3ea64f3799ce209cfeba215d
- Document Type :
- article
- Full Text :
- https://doi.org/10.1515/spma-2021-0156