{"title":"模糊图中一个顶点的邻域度的研究","authors":"Alimohammad Fallah Andevari","doi":"10.22457/apam.v26n2a03890","DOIUrl":null,"url":null,"abstract":". Graphs are one of the main tools for the mathematical modelling of various human problems. Fuzzy graphs clearly showed their ability to solve uncertain and ambiguous problems. Let G (cid:2) (cid:3)V, σ, μ(cid:8) be a fuzzy graph and u ∈ V . We define S (cid:12)(cid:13) (cid:3)u(cid:8) (cid:2) ∑ (cid:15)(cid:16)∈ℰ μ(cid:3)vu(cid:8)deg (cid:12) v . In this paper, we present some properties of S (cid:12)(cid:13) (cid:3)u(cid:8) on fuzzy graphs and establish relations between the Zagreb indices and the sum of the degrees of all neighbors of a vertex.","PeriodicalId":305863,"journal":{"name":"Annals of Pure and Applied Mathematics","volume":"25 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A Study on Degrees of all Neighbors of a Vertex in Fuzzy Graphs\",\"authors\":\"Alimohammad Fallah Andevari\",\"doi\":\"10.22457/apam.v26n2a03890\",\"DOIUrl\":null,\"url\":null,\"abstract\":\". Graphs are one of the main tools for the mathematical modelling of various human problems. Fuzzy graphs clearly showed their ability to solve uncertain and ambiguous problems. Let G (cid:2) (cid:3)V, σ, μ(cid:8) be a fuzzy graph and u ∈ V . We define S (cid:12)(cid:13) (cid:3)u(cid:8) (cid:2) ∑ (cid:15)(cid:16)∈ℰ μ(cid:3)vu(cid:8)deg (cid:12) v . In this paper, we present some properties of S (cid:12)(cid:13) (cid:3)u(cid:8) on fuzzy graphs and establish relations between the Zagreb indices and the sum of the degrees of all neighbors of a vertex.\",\"PeriodicalId\":305863,\"journal\":{\"name\":\"Annals of Pure and Applied Mathematics\",\"volume\":\"25 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1900-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Annals of Pure and Applied Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.22457/apam.v26n2a03890\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annals of Pure and Applied Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.22457/apam.v26n2a03890","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
A Study on Degrees of all Neighbors of a Vertex in Fuzzy Graphs
. Graphs are one of the main tools for the mathematical modelling of various human problems. Fuzzy graphs clearly showed their ability to solve uncertain and ambiguous problems. Let G (cid:2) (cid:3)V, σ, μ(cid:8) be a fuzzy graph and u ∈ V . We define S (cid:12)(cid:13) (cid:3)u(cid:8) (cid:2) ∑ (cid:15)(cid:16)∈ℰ μ(cid:3)vu(cid:8)deg (cid:12) v . In this paper, we present some properties of S (cid:12)(cid:13) (cid:3)u(cid:8) on fuzzy graphs and establish relations between the Zagreb indices and the sum of the degrees of all neighbors of a vertex.
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