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Extremal Matching Energy and the Largest Matching Root of Complete Multipartite Graphs
- 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).
- Subjects :
- Electronic computers. Computer science
QA75.5-76.95
Subjects
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