Some observations on the smallest adjacency eigenvalue of a graph
Combinatorics
2019-12-10 v1 Discrete Mathematics
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.
Cite
@article{arxiv.1912.03957,
title = {Some observations on the smallest adjacency eigenvalue of a graph},
author = {Sebastian M. Cioabă and Randall J. Elzinga and David A. Gregory},
journal= {arXiv preprint arXiv:1912.03957},
year = {2019}
}
Comments
24 pages, Discussiones Mathematicae Graph Theory, Special Issue in honor of Slobodan K. Simi\'c, accepted for publication