Authors: Feng, Lihua
Lu, Lu
Réti, Tamás
Stevanović, Dragan 
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: A bound on the spectral radius of graphs in terms of their Zagreb indices
Journal: Linear Algebra and Its Applications
Volume: 597
First page: 33
Last page: 45
Issue Date: 15-Jul-2020
Rank: M21
ISSN: 0024-3795
DOI: 10.1016/j.laa.2020.03.021
Abstract: 
The first and the second Zagreb index of a graph, usually defined as the sum of the squares of degrees over all vertices and the sum of the products of degrees of edge endvertices over all edges, respectively, are tightly related to the numbers of walks of length two and three in the graph. We provide here a lower bound on the spectral radius of adjacency matrix A of graph in terms of its Zagreb indices, based on the properties of the least square approximation of the vector A2j with the vectors Aj and j, where j is the all-one vector. The bound is sharp for all graphs with two main eigenvalues, surpassing the range of sharpness of other bounds among connected graphs.
Keywords: Main eigenvalues | Number of walks | Rayleigh quotient | Zagreb indices
Publisher: Elsevier
Project: NSFC (Nos. 11671402, 11871479)
Hunan Provincial Natural Science Foundation (Nos. 2016JJ2138, 2018JJ2479)
Graph theory and mathematical programming with applications in chemistry and computer science 

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