Authors: Alazemi, Abdullah
Anđelić, Milica
Simić, Slobodan 
Title: On the spectral invariants of symmetric matrices with applications in the spectral graph theory
Journal: Filomat
Volume: 31
Issue: 10
First page: 2925
Last page: 2932
Issue Date: 1-Jan-2017
Rank: M22
ISSN: 0354-5180
DOI: 10.2298/FIL1710925A
Abstract: 
We first prove a formula which relates the characteristic polynomial of a matrix (or of a weighted graph), and some invariants obtained from its principal submatrices (resp. vertex deleted subgraphs). Consequently, we express the spectral radius of the observed objects in the form of power series. In particular, as is relevant for the spectral graph theory, we reveal the relationship between spectral radius of a simple graph and its combinatorial structure by counting certain walks in any of its vertex deleted subgraphs. Some computational results are also included in the paper.
Keywords: Characteristic polynomial | Graph walks | Spectral radius | Symmetric matrix | Weighted graph
Publisher: Faculty of Sciences and Mathematics, University of Niš
Project: Kuwait University Research, Grant No. SM03/15

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