{"title":"Some remarks on the sum of powers of the degrees of graphs","authors":"E. Milovanovic, M. Matejic, I. Milovanovic","doi":"10.22108/TOC.2020.122877.1726","DOIUrl":null,"url":null,"abstract":"Let $G=(V,E)$ be a simple graph with $nge 3$ vertices, $m$ edges and vertex degree sequence $Delta=d_1 ge d_2 ge cdots ge d_n=delta>0$. Denote by $S={1, 2,ldots,n}$ an index set and by $J={I=(r_1, r_2,ldots,r_k) , | , 1le r_1<r_2<cdots<r_kle n}$ a set of all subsets of $S$ of cardinality $k$, $1le kle n-1$. In addition, denote by $d_{I}=d_{r_1}+d_{r_2}+cdots+d_{r_k}$, $1le kle n-1$, $1le r_1<r_2<cdots<r_kle n-1$, the sum of $k$ arbitrary vertex degrees, where $Delta_{I}=d_{1}+d_{2}+cdots+d_{k}$ and $delta_{I}=d_{n-k+1}+d_{n-k+2}+cdots+d_{n}$. We consider the following graph invariant $S_{alpha,k}(G)=sum_{Iin J}d_I^{alpha}$, where $alpha$ is an arbitrary real number, and establish its bounds. A number of known bounds for various topological indices are obtained as special cases.","PeriodicalId":43837,"journal":{"name":"Transactions on Combinatorics","volume":"10 1","pages":"63-71"},"PeriodicalIF":0.6000,"publicationDate":"2021-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Transactions on Combinatorics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.22108/TOC.2020.122877.1726","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
Let $G=(V,E)$ be a simple graph with $nge 3$ vertices, $m$ edges and vertex degree sequence $Delta=d_1 ge d_2 ge cdots ge d_n=delta>0$. Denote by $S={1, 2,ldots,n}$ an index set and by $J={I=(r_1, r_2,ldots,r_k) , | , 1le r_1
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