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SOME OBSERVATIONS ON THE SMALLEST ADJACENCY EIGENVALUE OF A GRAPH.
- Source :
-
Discussiones Mathematicae: Graph Theory . 2020, Vol. 40 Issue 2, p467-493. 27p. - Publication Year :
- 2020
-
Abstract
- In this paper, we discuss various connections between the smallest eigenvalue of the adjacency matrix of a graph and its structure. There are several techniques for obtaining upper bounds on the smallest eigenvalue, and some of them are based on Rayleigh quotients, Cauchy interlacing using induced subgraphs, and Haemers interlacing with vertex partitions and quotient matrices. In this paper, we are interested in obtaining lower bounds for the smallest eigenvalue. Motivated by results on line graphs and generalized line graphs, we show how graph decompositions can be used to obtain such lower bounds. [ABSTRACT FROM AUTHOR]
- Subjects :
- *RAYLEIGH quotient
*SUBGRAPHS
*EIGENVALUES
Subjects
Details
- Language :
- English
- ISSN :
- 12343099
- Volume :
- 40
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- Discussiones Mathematicae: Graph Theory
- Publication Type :
- Academic Journal
- Accession number :
- 141502267
- Full Text :
- https://doi.org/10.7151/dmgt.2285