The Maximal Matching Energy of Tricyclic Graphs
The Maximal Matching Energy of Tricyclic Graphs
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发表时间：
2014-09
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通讯作者：
Lin Chen;Yongtang Shi
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作者：
Lin Chen;Yongtang Shi
Gutman和瓦格纳提出了匹配能的概念，指出匹配能的化学应用可以追溯到20世纪70年代。设G是一个n阶简单图，1; 2;：：：; n是它的匹配多项式的根. G的匹配能量被定义为i（i = 1; 2;：;n）的绝对值之和。Gutman和Cvetkovi c通过计算机搜索n的小值并通过归纳论证确定了具有最大匹配数的n个顶点上的三环图。基于这一结果，本文刻画了所有三环图中匹配能量最大的图，并完全确定了具有最大匹配能量的三环图。我们利用匹配能量的Coulson型积分公式证明了我们的结果，这类似于比较两个准序不可比图的能量的方法。
Gutman and Wagner proposed the concept of the matching energy (ME) and pointed out that the chemical applications of ME go back to the 1970s. Let G be a simple graph of order n and 1; 2;:::; n be the roots of its matching polynomial. The matching energy of G is dened to be the sum of the absolute values of i (i = 1; 2;:::;n). Gutman and Cvetkovi c determined the tricyclic graphs on n vertices with maximal number of matchings by a computer search for small values of n and by an induction argument for the rest. Based on this result, in this paper, we characterize the graphs with the maximal value of matching energy among all tricyclic graphs, and completely determine the tricyclic graphs with the maximal matching energy. We prove our result by using Coulson-type integral formula of matching energy, which is similar as the method to comparing the energies of two quasi-order incomparable graphs.