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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Wiley
2019-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2019/9728976 |
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| author | Xiaolin Chen Huishu Lian |
| author_facet | Xiaolin Chen Huishu Lian |
| author_sort | Xiaolin Chen |
| collection | DOAJ |
| description | 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). |
| format | Article |
| id | doaj-art-df3f470bdb5a409c83ec00ecf5faef54 |
| institution | Kabale University |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2019-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-df3f470bdb5a409c83ec00ecf5faef542025-02-03T06:04:47ZengWileyComplexity1076-27871099-05262019-01-01201910.1155/2019/97289769728976Extremal Matching Energy and the Largest Matching Root of Complete Multipartite GraphsXiaolin Chen0Huishu Lian1Department of Mathematics, China University of Mining and Technology, Xuzhou 221116, ChinaDepartment of Mathematics, China University of Mining and Technology, Xuzhou 221116, ChinaThe 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).http://dx.doi.org/10.1155/2019/9728976 |
| spellingShingle | Xiaolin Chen Huishu Lian Extremal Matching Energy and the Largest Matching Root of Complete Multipartite Graphs Complexity |
| title | Extremal Matching Energy and the Largest Matching Root of Complete Multipartite Graphs |
| title_full | Extremal Matching Energy and the Largest Matching Root of Complete Multipartite Graphs |
| title_fullStr | Extremal Matching Energy and the Largest Matching Root of Complete Multipartite Graphs |
| title_full_unstemmed | Extremal Matching Energy and the Largest Matching Root of Complete Multipartite Graphs |
| title_short | Extremal Matching Energy and the Largest Matching Root of Complete Multipartite Graphs |
| title_sort | extremal matching energy and the largest matching root of complete multipartite graphs |
| url | http://dx.doi.org/10.1155/2019/9728976 |
| work_keys_str_mv | AT xiaolinchen extremalmatchingenergyandthelargestmatchingrootofcompletemultipartitegraphs AT huishulian extremalmatchingenergyandthelargestmatchingrootofcompletemultipartitegraphs |