两种分裂点连接运算图的Randic谱  

The Randic Spectrum of Two Types of Splitting-Vertex Join Graphs

作　　者：卢志琴 马小玲[1] LU Zhiqin;MA Xiaoling(School of Mathematics and System Sciences,Xinjiang University,Urumqi Xinjiang 830017,China)

机构地区：[1]新疆大学数学与系统科学学院,新疆乌鲁木齐830017

出　　处：《新疆大学学报（自然科学版）（中英文）》2022年第5期550-559,共10页Journal of Xinjiang University(Natural Science Edition in Chinese and English)

基　　金：新疆维吾尔自治区自然科学基金(2021D01C069);新疆维吾尔自治区优秀青年科技人才项目(2019Q016);新疆维吾尔自治区高校科研计划(XJEDU2021I001)。

摘　　要：对一个连通正则图G_(1)与任意一个正则图G_(2),基于分裂图SP(G_(1))与图G_(2)的两种运算,考虑对应新图类的Randic(规范化拉普拉斯,规范化无符号拉普拉斯)谱.利用这些结果,构造了关于上述三个矩阵的非正则的同谱图,并且计算了新构造图的度基尔霍夫指数和生成树的数目.For a connected regular graph G_(1) and an arbitrary regular graph G_(2),we determine the Randic(respectively,normalized Laplacian and normalized signless Laplacian)spectra of two types of graph operations on G_(1) and G_(2) involving the SP-graph of G_(1).Moreover,applying these results,we construct some non-regular simultaneous cospectral graphs for the Randic,normalized Laplacian and normalized signless Laplacian matrices,and compute the degree Kirchhof index and the number of spanning trees of the newly constructed graphs.

关 键 词：Randic谱 规范化拉普拉斯谱 规范化无符号拉普拉斯谱 分裂图 同谱图 度基尔霍夫指数 生成树数目 

分 类 号：O157.5[理学—数学]