{"docId":10271,"paperId":9432,"url":"https:\/\/dmtcs.episciences.org\/9432","doi":"10.46298\/dmtcs.9432","journalName":"Discrete Mathematics & Theoretical Computer Science","issn":"","eissn":"1365-8050","volume":[{"vid":658,"name":"vol. 24, no 2"}],"section":[{"sid":9,"title":"Graph Theory","description":[]}],"repositoryName":"arXiv","repositoryIdentifier":"2201.09269","repositoryVersion":3,"repositoryLink":"https:\/\/arxiv.org\/abs\/2201.09269v3","dateSubmitted":"2022-05-06 11:06:30","dateAccepted":"2022-10-24 08:37:54","datePublished":"2022-11-30 08:46:27","titles":["Proximity, remoteness and maximum degree in graphs"],"authors":["Dankelmann, Peter","Mafunda, Sonwabile","Mallu, Sufiyan"],"abstracts":["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.","Comment: 20 pages"],"keywords":["Mathematics - Combinatorics","05C12"]}