{"title":"RELATIONS BETWEEN ARITHMETIC-GEOMETRIC INDEX AND\nGEOMETRIC-ARITHMETIC INDEX","authors":"K. Das, Tomas Vetrik, MO YONG-CHEOL","doi":"10.59277/mrar.2024.26.76.1.17","DOIUrl":null,"url":null,"abstract":"The arithmetic-geometric index AG(G) and the geometric-arithmetic index\nGA(G) of a graph G are defined as AG(G) = P uv∈E(G) dG(u)+dG(v)\n2\n√\ndG(u)dG(v)\nand\nGA(G) =\nP\nuv∈E(G)\n2\n√\ndG(u)dG(v)\ndG(u)+dG(v) , where E(G) is the edge set of G, and dG(u)\nand dG(v) are the degrees of vertices u and v, respectively. We study relations\nbetween AG(G) and GA(G) for graphs G of given size, minimum degree and\nmaximum degree. We present lower and upper bounds on AG(G) + GA(G),\nAG(G) − GA(G) and AG(G) · GA(G). All the bounds are sharp.","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.59277/mrar.2024.26.76.1.17","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
The arithmetic-geometric index AG(G) and the geometric-arithmetic index
GA(G) of a graph G are defined as AG(G) = P uv∈E(G) dG(u)+dG(v)
2
√
dG(u)dG(v)
and
GA(G) =
P
uv∈E(G)
2
√
dG(u)dG(v)
dG(u)+dG(v) , where E(G) is the edge set of G, and dG(u)
and dG(v) are the degrees of vertices u and v, respectively. We study relations
between AG(G) and GA(G) for graphs G of given size, minimum degree and
maximum degree. We present lower and upper bounds on AG(G) + GA(G),
AG(G) − GA(G) and AG(G) · GA(G). All the bounds are sharp.
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