一些由(无符号)拉普拉斯谱所确定的图类  

Some graphs determined by their(signless) Laplacian spectra

作　　者：许剑锐 刘木伙[2] XU Jian-rui;LIU Mu-huo(Teaching Department of Information and Mechanical Engineering,Guangzhou Construction Engineering Vocational School,Guangzhou 510403,China;Department of Mathematics,College of Mathematics and Informations,South China Agricultural University,Guangzhou 510642,China)

机构地区：[1]广州市建筑工程职业学校信息与机电教学部,广东广州510403 [2]华南农业大学数学与信息学院数学系,广东广州510642

出　　处：《高校应用数学学报（A辑）》2018年第4期465-469,共5页Applied Mathematics A Journal of Chinese Universities(Ser.A)

基　　金：国家自然科学基金(11571123);广东省高等学校优秀青年教师培养计划(YQ2015027);广东省数据科学工程技术研究中心开放课题(2017A-KF02);广东省教育厅特色创新类项目(2017KTSCX020);2018年度国家级大学生创新创业训练计划(201810564014)

摘　　要：设G是一个n阶图而H是任意一个图.符号G?H表示由G和n个顶点不交的图H通过把G的第i个顶点和第i个H的所有顶点都连一条边所得的图,其中1≤i≤n.设p≥3和q为两个正整数.令Cp和Kp分别表示p个顶点的圈和完全图.证明了Cp?qK_1和Kp?qK_1分别被它们的拉普拉斯图谱所确定,且当p为奇数时Cp?qK_1也被它的无符号拉普拉斯图谱所确定.文中的结果推广了[Bu Changjiang, et al.,(2014),Graphs Combin, 30:1123-1133],[Boulet R (2009). Discrete Math Theor Comput Sci, 11:149-160]和[Mirzakhah M, Kiani D (2010). Electron J Linear Algebra, 20:610-620]的相应结论.Let G be a graph with n vertices and H be an arbitrary graph.Let G○H be the graph obtained from G and n copies of H by joining the i-th vertex of G to each vertex in the i-th copy of H,where 1≤i≤n.Let p≥3 and q be two positive integers.Denote by Cp and Kp the cycle and complete graph with p vertices,respectively.The paper proves that Cp○qK1 and Kp○qK1 are determined by their Laplacian spectra,respectively,and Cp○qK1 is also determined by its signless Laplacian spectrum for odd integer p.The results extend the corresponding results of[Bu Changjiang,et al.,(2014),Graphs Combin,30:1123-1133],[Boulet R(2009).Discrete Math Theor Comput Sci,11:149-160]and[Mirzakhah M,Kiani D(2010).Electron J Linear Algebra,20:610-620],respectively.

关 键 词：图谱的确定性 (无符号)拉普拉斯图谱 单圈图 

分 类 号：O157.5[理学—数学]