{"title":"图的乘性Sombor指数","authors":"Hechao Liu","doi":"10.47443/dml.2021.s213","DOIUrl":null,"url":null,"abstract":"The Sombor index of a graph G is defined as SO ( G ) = (cid:80) uv ∈ E ( G ) (cid:112) d 2 G ( u ) + d 2 G ( v ) , where d G ( u ) denotes the degree of the vertex u of G . Accordingly, the multiplicative Sombor index of G can be defined as (cid:81) SO ( G ) = (cid:81) uv ∈ E ( G ) (cid:112) d 2 G ( u ) + d 2 G ( v ) . In this article, some graph transformations which increase or decrease the multiplicative Sombor index are first introduced. Then by using these transformations, extremal values of the multiplicative Sombor index of trees and unicyclic graphs are determined.","PeriodicalId":36023,"journal":{"name":"Discrete Mathematics Letters","volume":" ","pages":""},"PeriodicalIF":1.0000,"publicationDate":"2022-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"Multiplicative Sombor Index of Graphs\",\"authors\":\"Hechao Liu\",\"doi\":\"10.47443/dml.2021.s213\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The Sombor index of a graph G is defined as SO ( G ) = (cid:80) uv ∈ E ( G ) (cid:112) d 2 G ( u ) + d 2 G ( v ) , where d G ( u ) denotes the degree of the vertex u of G . Accordingly, the multiplicative Sombor index of G can be defined as (cid:81) SO ( G ) = (cid:81) uv ∈ E ( G ) (cid:112) d 2 G ( u ) + d 2 G ( v ) . In this article, some graph transformations which increase or decrease the multiplicative Sombor index are first introduced. Then by using these transformations, extremal values of the multiplicative Sombor index of trees and unicyclic graphs are determined.\",\"PeriodicalId\":36023,\"journal\":{\"name\":\"Discrete Mathematics Letters\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":1.0000,\"publicationDate\":\"2022-03-28\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Discrete Mathematics Letters\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.47443/dml.2021.s213\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Discrete Mathematics Letters","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.47443/dml.2021.s213","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
The Sombor index of a graph G is defined as SO ( G ) = (cid:80) uv ∈ E ( G ) (cid:112) d 2 G ( u ) + d 2 G ( v ) , where d G ( u ) denotes the degree of the vertex u of G . Accordingly, the multiplicative Sombor index of G can be defined as (cid:81) SO ( G ) = (cid:81) uv ∈ E ( G ) (cid:112) d 2 G ( u ) + d 2 G ( v ) . In this article, some graph transformations which increase or decrease the multiplicative Sombor index are first introduced. Then by using these transformations, extremal values of the multiplicative Sombor index of trees and unicyclic graphs are determined.
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