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

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-...

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Bibliographic Details
Main Authors: Xiaolin Chen, Huishu Lian
Format: Article
Language:English
Published: Wiley 2019-01-01
Series:Complexity
Online Access:http://dx.doi.org/10.1155/2019/9728976
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Summary: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).
ISSN:1076-2787
1099-0526