The bipartite unicyclic graphs with the first largest matching energies

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• 作者：Lin Chen ^{chenlin1120120012@126.com" class="auth_mail" title="E-mail the corresponding author} ; Jinfeng Liu ; ^{ljinfeng709@163.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Matching energy ; Bipartite unicyclic graphs ; Quasi-order ; Coulson integral formula
• 刊名：Applied Mathematics and Computation
• 出版年：2015
• 出版时间：1 October 2015
• 年：2015
• 卷：268
• 期：Complete
• 页码：644-656
• 全文大小：541 K

文摘

The theory of matching energy of graphs since been proposed by Gutman and Wagner in 2012, has attracted more and more attention. It is denoted by B_n,m,${\mathcal{B}}_{n,m,}$ the class of bipartite graphs with order n and size m  . In particular, B_n,n${\mathcal{B}}_{n,n}$ denotes the set of bipartite unicyclic graphs, which is an interesting class of graphs. In this paper, for odd n  , we characterize the bipartite unicyclic graphs with the first $\lfloor \frac{n-3}{4}\rfloor$ largest matching energies. There is an interesting correspondence: we conclude that the graph with the second maximal matching energy in B_n,n${\mathcal{B}}_{n,n}$ for odd n   ≥ 11 is $P_n^6,$ which is the only graph attaining the maximum value of the energy among all the (bipartite) unicyclic graphs for n ≥ 16.