{"title":"𝒫-energy of graphs","authors":"Prajakta Bharat Joshi, Mayamma Joseph","doi":"10.2478/ausi-2020-0009","DOIUrl":null,"url":null,"abstract":"Abstract Given a graph G = (V, E), with respect to a vertex partition 𝒫 we associate a matrix called 𝒫-matrix and define the 𝒫-energy, E𝒫 (G) as the sum of 𝒫-eigenvalues of 𝒫-matrix of G. Apart from studying some properties of 𝒫-matrix, its eigenvalues and obtaining bounds of 𝒫-energy, we explore the robust(shear) 𝒫-energy which is the maximum(minimum) value of 𝒫-energy for some families of graphs. Further, we derive explicit formulas for E𝒫 (G) of few classes of graphs with different vertex partitions.","PeriodicalId":41480,"journal":{"name":"Acta Universitatis Sapientiae Informatica","volume":"2014 1","pages":"137 - 157"},"PeriodicalIF":0.3000,"publicationDate":"2020-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Acta Universitatis Sapientiae Informatica","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2478/ausi-2020-0009","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"COMPUTER SCIENCE, THEORY & METHODS","Score":null,"Total":0}
引用次数: 0
Abstract
Abstract Given a graph G = (V, E), with respect to a vertex partition 𝒫 we associate a matrix called 𝒫-matrix and define the 𝒫-energy, E𝒫 (G) as the sum of 𝒫-eigenvalues of 𝒫-matrix of G. Apart from studying some properties of 𝒫-matrix, its eigenvalues and obtaining bounds of 𝒫-energy, we explore the robust(shear) 𝒫-energy which is the maximum(minimum) value of 𝒫-energy for some families of graphs. Further, we derive explicit formulas for E𝒫 (G) of few classes of graphs with different vertex partitions.
摘要:给定图G = (V, E),对一个顶点划分,我们关联一个矩阵𝒫-matrix,并定义𝒫-energy, E (G)为G的𝒫-matrix的𝒫-eigenvalues的和。除了研究𝒫-matrix的一些性质,它的特征值和𝒫-energy的界外,我们还探讨了图族中𝒫-energy的最大(最小)值的鲁棒性(剪切性)𝒫-energy。进一步,我们导出了几种不同顶点划分的图的显式公式E - p (G)。