I. Milovanovic, M. Matejic, P. Milošević, E. Milovanovic, Akbar Ali
{"title":"关于图的拉普拉斯能量的一些下界的注释","authors":"I. Milovanovic, M. Matejic, P. Milošević, E. Milovanovic, Akbar Ali","doi":"10.22108/TOC.2019.115269.1616","DOIUrl":null,"url":null,"abstract":"For a simple connected graph $G$ of order $n$ and size $m$, the Laplacian energy of $G$ is defined as $LE(G)=sum_{i=1}^n|mu_i-frac{2m}{n}|$ where $mu_1, mu_2,ldots,mu_{n-1}, mu_{n}$ are the Laplacian eigenvalues of $G$ satisfying $mu_1ge mu_2gecdots ge mu_{n-1}> mu_{n}=0$. In this note, some new lower bounds on the graph invariant $LE(G)$ are derived. The obtained results are compared with some already known lower bounds of $LE(G)$.","PeriodicalId":43837,"journal":{"name":"Transactions on Combinatorics","volume":"8 1","pages":"13-19"},"PeriodicalIF":0.6000,"publicationDate":"2019-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"A note on some lower bounds of the Laplacian energy of a graph\",\"authors\":\"I. Milovanovic, M. Matejic, P. Milošević, E. Milovanovic, Akbar Ali\",\"doi\":\"10.22108/TOC.2019.115269.1616\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"For a simple connected graph $G$ of order $n$ and size $m$, the Laplacian energy of $G$ is defined as $LE(G)=sum_{i=1}^n|mu_i-frac{2m}{n}|$ where $mu_1, mu_2,ldots,mu_{n-1}, mu_{n}$ are the Laplacian eigenvalues of $G$ satisfying $mu_1ge mu_2gecdots ge mu_{n-1}> mu_{n}=0$. In this note, some new lower bounds on the graph invariant $LE(G)$ are derived. The obtained results are compared with some already known lower bounds of $LE(G)$.\",\"PeriodicalId\":43837,\"journal\":{\"name\":\"Transactions on Combinatorics\",\"volume\":\"8 1\",\"pages\":\"13-19\"},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2019-06-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Transactions on Combinatorics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.22108/TOC.2019.115269.1616\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Transactions on Combinatorics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.22108/TOC.2019.115269.1616","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
A note on some lower bounds of the Laplacian energy of a graph
For a simple connected graph $G$ of order $n$ and size $m$, the Laplacian energy of $G$ is defined as $LE(G)=sum_{i=1}^n|mu_i-frac{2m}{n}|$ where $mu_1, mu_2,ldots,mu_{n-1}, mu_{n}$ are the Laplacian eigenvalues of $G$ satisfying $mu_1ge mu_2gecdots ge mu_{n-1}> mu_{n}=0$. In this note, some new lower bounds on the graph invariant $LE(G)$ are derived. The obtained results are compared with some already known lower bounds of $LE(G)$.
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