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The Signature of Chordal Graphs and Cographs
Graphs and Combinatorics ( IF 0.6 ) Pub Date : 2021-01-21 , DOI: 10.1007/s00373-021-02273-1
Changxiang He , Shujuan Qian , Haiying Shan , Baofeng Wu

The signature s(G) of a graph G is defined as the difference between its positive inertia index and negative inertia index. In 2013, Ma et al. conjectured that \(-c_3(G)\le s(G) \le c_5(G)\) for an arbitrary simple graph G, where \(c_3(G)\) denotes the number of cycles in G of length 3 modulo 4, \(c_5(G)\) denotes the number of cycles in G of length 1 modulo 4. In this paper, we give some inequalities of signature of graphs, as applications, we prove that this conjecture holds for chordal graphs and cographs.



中文翻译:

和弦图和图形的签名

曲线G的签名sG)被定义为其正惯性指数和负惯性指数之间的差。2013年,Ma等。推测\(-c_3(G)\ le s(G)\ le c_5(G)\)对于任意简单图G,其中\(c_3(G)\)表示长度为3模的G中的循环数4,\(c_5(G)\)表示长度为1模4的G中的循环数。。

更新日期:2021-01-21
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