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On the eigenvalues of Laplacian ABC-matrix of graphs.
- Source :
-
QM - Quaestiones Mathematicae . Nov2023, Vol. 46 Issue 11, p2403-2419. 17p. - Publication Year :
- 2023
-
Abstract
- For a simple graph G, the ABC-index is a degree based topological index and is defined as where dv is the degree of the vertex υ in G. Recently, the Laplacian ABC-matrix was introduced in [22] is defined by where is the diagonal matrix of ABC-degrees and Ã(G) is the ABC-matrix of G: The eigenvalues of the matrix are called the Laplacian ABC-eigenvalues of G. In the article, we consider the problem of characterization of connected graphs having exactly three distinct Laplacian ABC-eigenvalues. We solve this problem for bipartite graphs, multipartite graphs, unicyclic graphs, regular graphs and prove the non-existence of such graphs with diameter greater than 2. We introduce the concept of trace norm of the matrix called the Laplacian ABC-energy of G. We obtain some upper and lower bounds for the Laplacian ABC-energy and characterize the extremal graphs which attain these bounds. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 16073606
- Volume :
- 46
- Issue :
- 11
- Database :
- Academic Search Index
- Journal :
- QM - Quaestiones Mathematicae
- Publication Type :
- Academic Journal
- Accession number :
- 172994738
- Full Text :
- https://doi.org/10.2989/16073606.2022.2156405