{"title":"图中的接近度、距离和最大度","authors":"P. Dankelmann, Sonwabile Mafunda, Sufiyan Mallu","doi":"10.46298/dmtcs.9432","DOIUrl":null,"url":null,"abstract":"The average distance of a vertex $v$ of a connected graph $G$ is the\narithmetic mean of the distances from $v$ to all other vertices of $G$. The\nproximity $\\pi(G)$ and the remoteness $\\rho(G)$ of $G$ are the minimum and the\nmaximum of the average distances of the vertices of $G$, respectively.\n In this paper, we give upper bounds on the remoteness and proximity for\ngraphs of given order, minimum degree and maximum degree. Our bounds are sharp\napart from an additive constant.","PeriodicalId":110830,"journal":{"name":"Discret. Math. Theor. Comput. Sci.","volume":"27 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2022-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Proximity, remoteness and maximum degree in graphs\",\"authors\":\"P. Dankelmann, Sonwabile Mafunda, Sufiyan Mallu\",\"doi\":\"10.46298/dmtcs.9432\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The average distance of a vertex $v$ of a connected graph $G$ is the\\narithmetic mean of the distances from $v$ to all other vertices of $G$. The\\nproximity $\\\\pi(G)$ and the remoteness $\\\\rho(G)$ of $G$ are the minimum and the\\nmaximum of the average distances of the vertices of $G$, respectively.\\n In this paper, we give upper bounds on the remoteness and proximity for\\ngraphs of given order, minimum degree and maximum degree. Our bounds are sharp\\napart from an additive constant.\",\"PeriodicalId\":110830,\"journal\":{\"name\":\"Discret. Math. Theor. Comput. Sci.\",\"volume\":\"27 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2022-01-23\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Discret. Math. Theor. Comput. Sci.\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.46298/dmtcs.9432\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Discret. Math. Theor. Comput. Sci.","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.46298/dmtcs.9432","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Proximity, remoteness and maximum degree in graphs
The average distance of a vertex $v$ of a connected graph $G$ is the
arithmetic mean of the distances from $v$ to all other vertices of $G$. The
proximity $\pi(G)$ and the remoteness $\rho(G)$ of $G$ are the minimum and the
maximum of the average distances of the vertices of $G$, respectively.
In this paper, we give upper bounds on the remoteness and proximity for
graphs of given order, minimum degree and maximum degree. Our bounds are sharp
apart from an additive constant.