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Extremal Matching Energy and the Largest Matching Root of Complete Multipartite Graphs

Authors :
Xiaolin Chen
Huishu Lian
Source :
Complexity, Vol 2019 (2019)
Publication Year :
2019
Publisher :
Hindawi-Wiley, 2019.

Abstract

The matching energy ME(G) of a graph G was introduced by Gutman and Wagner, which is defined as the sum of the absolute values of the roots of the matching polynomial m(G,x). The largest matching root λ1(G) is the largest root of the matching polynomial m(G,x). Let Kn1,n2,…,nr denote the complete r-partite graph with order n=n1+n2+…+nr, where r>1. In this paper, we prove that, for the given values n and r, both the matching energy ME(G) and the largest matching root λ1(G) of complete r-partite graphs are minimal for complete split graph CS(n,r-1) and are maximal for Turán graph T(n,r).

Details

Language :
English
ISSN :
10762787 and 10990526
Volume :
2019
Database :
Directory of Open Access Journals
Journal :
Complexity
Publication Type :
Academic Journal
Accession number :
edsdoj.f3f470bdb5a409c83ec00ecf5faef54
Document Type :
article
Full Text :
https://doi.org/10.1155/2019/9728976