广义线图与{C41,K1,31,K1,4}-free图的符号差  

The signature of generalized line graph and {C41,K1,31,K1,4}-free graph

作　　者：赵志敏 何常香[1] 徐光辉[2] ZHAO Zhi-min;HE Chang-xiang;XU Guang-hui(College of Science,University of Shanghai for Science and Technology,Shanghai 200093,China;College of Science,Zhejiang A&F University,Hangzhou 311300,China)

机构地区：[1]上海理工大学理学院,上海200093 [2]浙江农林大学理学院,浙江杭州311300

出　　处：《高校应用数学学报（A辑）》2019年第4期492-500,共9页Applied Mathematics A Journal of Chinese Universities(Ser.A)

摘　　要：图的邻接矩阵的正,负特征值个数分别被称为图的正,负惯性指数.图G的正惯性指数与负惯性指数之差被称为图G的符号差,记作s(G). 2013年马海成等人提出符号差猜想:对于任意简单图G,都有-c3(G)≤s(G)≤c5(G),其中ci(G)(i∈{3, 5})分别表示G中长为模4余3和模4余1的圈的个数.此文证明了广义线图和不含C41, K1,31,K1,4之一作为诱导子图的图满足此猜想.The positive(resp., negative) inertia index of G, denoted by p(G)(resp., n(G)), is defined to be the number of positive(resp., negative) eigenvalues of its adjacency matrix. The signature s(G) of a graph G is defined as the difference between its positive inertia index and negative inertia index. In 2013, H. Ma et al. conjectured that-c3(G) ≤ s(G) ≤ c5(G) for an arbitrary simple graph G, where c3(G) denotes the number of cycles in G of length 3 modulo 4, c5(G) denotes the number of cycles in G of length 1 modulo 4. The paper proves that this conjecture holds for generalized line graph and {C41, K1,31, K1,4}-free graph.

关 键 词：符号差 广义线图 诱导子图 惯性指数 

分 类 号：O157.5[理学—数学]