剖分Q-邻接冠图的广义特征多项式及其应用  

Generalized characteristic polynomial of subdivision Q-neighbourhood corona graphs and its application

作　　者：杨影 李沐春[1] 张友 YANG Ying;LI Mu-chun;ZHANG You(College of Mathematics and Physics,Lanzhou Jiaotong University,Lanzhou 730070,Gansu,China;College of Computer and Engineering,Shangqiu College,Shangqiu 476000,Henan,China)

机构地区：[1]兰州交通大学数理学院,甘肃兰州730070 [2]商丘学院计算机工程学院,河南商丘476000

出　　处：《山东大学学报（理学版）》2021年第7期65-72,81,共9页Journal of Shandong University(Natural Science)

基　　金：国家自然科学基金资助项目(11961041);甘肃省自然科学基金资助项目(17JR5RA099);兰州交通大学青年基金资助项目(2017004)。

摘　　要：设正则图G_(1)和G_(2)的剖分Q-邻接点冠图G_(1)■_(Q)G_(2)是由Q(G_(1))和|V(G_(1))|个点不交的G_(2)的拷贝,通过连接V(G_(1))中第i个顶点的所有邻点与第i个G_(2)的拷贝的所有点后得到的图;剖分Q-邻接边冠图G_(1)■_(Q)G_(2)是由Q(G_(1))和|I(G_(1))|个点不交的G_(2)的拷贝,通过连接I(G_(1))中第i个顶点的所有邻点与第i个G_(2)的拷贝的所有点后得到的图。其中Q(G_(1))是由图G_(1)的每条边上插入一个新点且当图G_(1)的2条边相邻时对应的2个新点之间连接一条边后得到的图,I(G_(1))是图G_(1)中每条边上插入的新点所构成的集合。分别确定了剖分Q-邻接点冠图G_(1)■_(Q)G_(2)和剖分Q-邻接边冠图G_(1)■_(Q)G_(2)的广义特征多项式及其相应的Φ-谱。得到了G_(1)■_(Q)G_(2)和G_(1)■_(Q)G_(2)的规范拉普拉斯谱,同时也构造了一些Φ-同谱无穷类。The subdivision Q-neighborhood vertex corona G_(1)■_(Q)G_(2) of two regular graphs G_(1) and G_(2) for regular is the graph obtained from vertex disjoint union of Q(G_(1)) and |V(G_(1))| copies of G_(2), and by joining the neighbors of the ith vertex of |V(G_(1))| to every vertex in the ith copy of G_(2);the subdivision Q-neighborhood edge corona G_(1)■_(Q)G_(2) is the graph obtained from vertex disjoint union of Q(G_(1)) and |I(G_(1))| copies of G_(2), and by joining the neighbors of the ith vertex of I(G_(1)) to every vertex in the ith copy of G_(2), where Q(G_(1)) is obtained from G_(1) by inserting a new vertex into every edge of G_(1) and then joining by edges those pair of new vertices which lie on adjacent edges of G_(1), and I(G_(1)) is denoted by the set of such new vertices inserted in each edge of G_(1). Based on above, the generalized characteristic polynomial and Φ-spectrum of G_(1)■_(Q)G_(2) and G_(1)■_(Q)G_(2) are determined, respectively. As an application, their normalized Laplacian spectrum are obtained. Besides, infinitely many pairs of Φ-cospectral mates are also constructed.

关 键 词：剖分Q-邻接点冠图 剖分Q-邻接边冠图 广义特征多项式 Φ-同谱图 

分 类 号：O157.5[理学—数学]