{"title":"Sombor Index of Hypergraphs","authors":"Shashwath S Shetty, K. Arathi Bhat","doi":"10.46793/match.91-1.235s","DOIUrl":null,"url":null,"abstract":"Recently, the Sombor index of a graph was defined, and a large amount of study was conducted quite quickly. It has been proposed to generalise the idea of vertex degree-based topological indices from graphs to hypergraphs. We give the bounds for the Sombor index of hypergraphs and bipartite hypergraphs using the total number of vertices in the graph. Hypertrees are the connected hypergraph, where the removal of any hyperedge disconnects the hypergraph. A -uniform hypergraph is a hypergraph with k vertices in every hyperedge and a linear hypergraph is a hypergraph where any two hyperedges can have at most one vertex in common. We give the extremal hypergraphs among the class of uniform, linear and general hypertrees. The expected generalisation of some vertex degree based topological indices from graphs to hypergraphs has been listed.","PeriodicalId":51115,"journal":{"name":"Match-Communications in Mathematical and in Computer Chemistry","volume":null,"pages":null},"PeriodicalIF":2.9000,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Match-Communications in Mathematical and in Computer Chemistry","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.46793/match.91-1.235s","RegionNum":2,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
Abstract
Recently, the Sombor index of a graph was defined, and a large amount of study was conducted quite quickly. It has been proposed to generalise the idea of vertex degree-based topological indices from graphs to hypergraphs. We give the bounds for the Sombor index of hypergraphs and bipartite hypergraphs using the total number of vertices in the graph. Hypertrees are the connected hypergraph, where the removal of any hyperedge disconnects the hypergraph. A -uniform hypergraph is a hypergraph with k vertices in every hyperedge and a linear hypergraph is a hypergraph where any two hyperedges can have at most one vertex in common. We give the extremal hypergraphs among the class of uniform, linear and general hypertrees. The expected generalisation of some vertex degree based topological indices from graphs to hypergraphs has been listed.
期刊介绍：
MATCH Communications in Mathematical and in Computer Chemistry publishes papers of original research as well as reviews on chemically important mathematical results and non-routine applications of mathematical techniques to chemical problems. A paper acceptable for publication must contain non-trivial mathematics or communicate non-routine computer-based procedures AND have a clear connection to chemistry. Papers are published without any processing or publication charge.
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