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| 摘要: |
| 设G是有n个点的图，在G的所有特征根中，正特征根的个数和负特征根的个数分别称为图G的正惯性指数和负惯性指数，分别记为p（G）和n（G）.这两个参数密切联系与图G的零度，而图的零度是具有重要化学应用的图参数，特别是对分子图，它已经被大量的研究.这篇文章的主要目的是刻画具有小的负惯性指数的图.利用图的点繁殖运算，刻画了具有n（G）≤ 2的所有图，也刻画了具有n（G）≤ 3的带有悬挂点的所有图. |
| 关键词: 正惯性指数 负惯性指数 点繁殖 |
| DOI： |
| 分类号:O157.5 |
| 基金项目:Supported by National Natural Science Foundation of China (11561056); Natural Science Foundation of Qinghai Provence (2016-ZJ-914). |
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| GRAPHS WITH SMALL NEGATIVE INERTIA INDEX |
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MA Hai-cheng,XIE Cheng-ling,LI Dan-yang
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| Abstract: |
| For a graph G with order n, the number of positive and negative eigenvalues of G, denoted by p(G) and n(G), respectively, are called the positive and negative inertia indices of G. The inertia indices are closely related to the nullity of the graph, which has important applications in chemistry， and is intensively studied, especially for molecular graphs. The main objective of this paper is to determine the structure of graphs with small negative inertia index. By utilizing vertex multiplications, we obtain a characterization for graphs G with n(G) ≤ 2, as well as for graphs G with pendent vertices and with n(G) ≤ 3. |
| Key words: positive inertia index negative inertia index multiplication of vertices |
