两种分裂点连接运算图的Randi?谱

卢志琴; 马小玲

doi:10.13568/j.cnki.651094.651316.2021.11.16.0002

您当前的位置：

首页 >

文章列表页 >

两种分裂点连接运算图的Randi?谱

更新时间：2026-01-21

- 两种分裂点连接运算图的Randi?谱
- Journal of Xinjiang University (Natural Science Edition in Chinese and English) Vol. 39, Issue 5, Pages: 550-559(2022)
- 作者机构：
  
  新疆大学数学与系统科学学院
- 作者简介：
- 基金信息：
- DOI：10.13568/j.cnki.651094.651316.2021.11.16.0002
  CLC： O157.5
- Published：2022
- 稿件说明：
移动端阅览
[1]卢志琴,马小玲.两种分裂点连接运算图的Randi?谱[J].新疆大学学报(自然科学版)(中英文),2022,39(05):550-559.
[1]卢志琴,马小玲.两种分裂点连接运算图的Randi?谱[J].新疆大学学报(自然科学版)(中英文),2022,39(05):550-559. DOI： 10.13568/j.cnki.651094.651316.2021.11.16.0002.

DOI：10.13568/j.cnki.651094.651316.2021.11.16.0002.

摘要

对一个连通正则图G1与任意一个正则图G2

基于分裂图SP (G1)与图G2的两种运算

考虑对应新图类的Randi?(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.

Abstract

For a connected regular graph G1 and an arbitrary regular graph G2

we determine the Randi?(respectively

normalized Laplacian and normalized signless Laplacian) spectra of two types of graph operations on G1 and G2 involving the SP-graph of G1. Moreover

applying these results

we construct some non-regular simultaneous cospectral graphs for the Randi?

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

Keywords

references

RANDIC M.Characterization of molecular branching[J].Journal of the American Chemical Society,1975,97(23):6609-6615.

BOZKURT B,GUUNGOR A D,GUTMAN I,et al.Randi? matrix and randic energy[J].Match Communications in Mathematical and in Computer Chemistry,2010,64(1):239-250.

GUTMAN I,FURTULA B,BOZKURT B.On Randi? energy[J].Linear Algebra and Its Applications,2014,442(1):50-57.

BARIK S,BAPAT R B,PATI S.On the Laplacian spectra of product graphs[J].Applicable Analysis and Discrete Mathematics,2015,9:39-58.

AYGUL M,QIN X J.A note on the integrity of the corona and edge corona of two graphs[J].Journal of Xinjiang University(Natural Science Edition),2013,30(3):278-281.

LIN X,ELKIN V,BIAN H.The wiener polarity index of graph operations[J].Journal of Xinjiang University(Natural Science Edition),2013,30(1):55-60.

CHENG L L,HUANG Q X.The adjacency spectrum of the corona graph G1?Km1,m2[J].Journal of Xinjiang University(Natural Science Edition),2011,28(2):156-162.

HOU Y,SHIU W C.The spectrum of the edge corona of two graphs[J].The Electronic Journal of Linear Algebra,2010,20(1):586-594.

GOPALAPILLAI I.The spectrum of neighborhood corona of graphs[J].Kragujevac Journal of Mathematics,2011,35(3):493-500.

HARARY F.Graph theory[M].Massachusetts:Addison-Wesley,1994.

SAMPATHKUMAR E,WALIKAR H B.On the splitting graph of a graph[J].Journal of the Karnatak University Science,1981,35/36:13-16.

ZHANG F Z.The schur complement and its applications[M].New York:Springer,2005.

DAS A,PANIGRAHI P.New classes of simultaneous cospectral graphs for adjacency,laplacian and normalized laplacian matrices[J].Kragujevac Journal of Mathematics,2019,43(2):303-323.

KLEIN D J,RANDIC M.Resistance distance[J].Journal of Mathematical Chemistry,1993,12(1):81-95.

CHEN A H,ZHANG B F.Resistance distance and the normalized Laplacian spectrum[J].Discrete Applied Mathematics,2007,155(5):654-661.

FENG L,GUTMAN I,YU G.Degree Kirchhoff index of unicyclic graphs[J].Match Communications in Mathematical and in Computer Chemistry,2013,69(3):629-648.

HUANG J,LI S C.On the normalized Laplacian,degree-Kirchhoff index and spanning trees of graphs[J].Bulletin of the Australian Mathematical Society,2015,91(3):353-367．

CHUNG F R K.Spectral graph theory[M].Rhode Island:American Mathematical Society,1997.

CUI S Y,TIAN G X.The spectrum and the signless Laplacian spectrum of corona[J].Linear Algebra and Its Applications,2012,437(7):1692-1703.

Views

下载量

CSCD

Alert me when the article has been cited

提交

Tools

Publicity Resources

带有一条悬挂边的沙漏图的谱的刻画（英文）

Related Author

秦正新

张文丽

孟吉翔

Related Institution

新疆师范大学数学科学学院

⁰