第44卷第2期2023年2月哈尔滨工程大学学报JournalofHarbinEngineeringUniversityVol.44№.2Feb.2023路矩阵相关谱半径和路谱展的界及其应用卢鹏丽,栾睿(兰州理工大学计算机与通信学院,甘肃兰州730050)摘要:由于图谱能够很好地反映图的结构性质且便于计算,本文通过图的矩阵,建立图谱与图的拓扑性质之间的联系,更好地反应图的结构和研究图的相关性质;利用矩阵论和图论的理论和方法,证明路谱半径的下界和路无符号拉普拉斯谱半径的上下界;定义路谱展并得到其上下界;最后作为应用,研究完全r-部图的路谱、路拉普拉斯谱和路无符号拉普拉斯谱并得到了图Kp,p,…,p的相关能量。关键词:路矩阵;路谱展;路谱半径;能量;路无符号拉普拉斯谱半径;完全r-部图;路谱;路(无符号)拉普拉斯谱DOI:10.11990/jheu.202106018网络出版地址:https://kns.cnki.net/kcms/detail/23.1390.U.20221103.1153.004.html中图分类号:O157.5,O157.6文献标志码:A文章编号:1006-7043(2023)02-0251-06BoundsofcorrelationspectrumradiusofpathmatrixandpathspectrumspreadandtheirapplicationsLUPengli,LUANRui(SchoolofComputerandCommunication,LanzhouUniversityofTechnology,Lanzhou730050,China)Abstract:Thegraphspectrumcanwellreflectthestructuralpropertiesofgraphsandiseasytocalculate.Inthispaper,therelationshipbetweengraphspectrumandtopologicalpropertiesofgraphisestablishedbythematrixofgraph,soastobetterreflectthestructureofgraphandstudyrelatedpropertiesofthegraph.Usingthetheoryandmethodofmatrixtheoryandgraphtheory,weprovethelowerboundofthepathspectrumradiusandtheupperandlowerboundsofthepathsignlessLaplacianspectrumradius.Wedefinethepathspectrumspreadandgettheupperandlowerbounds.Finally,asanapplication,westudythecompleter-partitegraph,getthepathspectrum,pathLaplacianspectrumandpathsignlessLaplacianspectrumandrelatedenergyofKp,p,…,p.Keywords:pathmatrix;pathspectrumspread;pathspectrumradius;energy;pathsignlessLaplacianspectrumra-dius;completer-partitegraph;pathspectrum;path(signless)Laplacianspectrum收稿日期:2021-06-18.网络出版日期:2022-11-03.基金项目:国家自然科学基金项目(11861045,62162040).作者简介:卢鹏丽,女,教授,博士生导师.通信作者:卢鹏丽,E-mail:lupengli88@163.com.代数图论是采用代数方法解决图...
