{"title":"几类图的奇调和标记","authors":"P. Jeyanthi, S. Philo","doi":"10.4067/s0719-06462020000300299","DOIUrl":null,"url":null,"abstract":"A graph G ( p, q ) is said to be odd harmonious if there exists an injection f : V ( G ) → { 0 , 1 , 2 , · · · , 2 q − 1 } such that the induced function f ∗ : E ( G ) → { 1 , 3 , · · · , 2 q − 1 } defined by f ∗ ( uv ) = f ( u ) + f ( v ) is a bijection. In this paper we prove that T p - tree, T ˆ ◦ P m , T ˆ ◦ 2 P m , regular bamboo tree, C n ˆ ◦ P m , C n ˆ ◦ 2 P m and subdivided grid graphs are odd harmonious.","PeriodicalId":36416,"journal":{"name":"Cubo","volume":" ","pages":""},"PeriodicalIF":0.5000,"publicationDate":"2020-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Odd Harmonious Labeling of Some Classes of Graphs\",\"authors\":\"P. Jeyanthi, S. Philo\",\"doi\":\"10.4067/s0719-06462020000300299\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"A graph G ( p, q ) is said to be odd harmonious if there exists an injection f : V ( G ) → { 0 , 1 , 2 , · · · , 2 q − 1 } such that the induced function f ∗ : E ( G ) → { 1 , 3 , · · · , 2 q − 1 } defined by f ∗ ( uv ) = f ( u ) + f ( v ) is a bijection. In this paper we prove that T p - tree, T ˆ ◦ P m , T ˆ ◦ 2 P m , regular bamboo tree, C n ˆ ◦ P m , C n ˆ ◦ 2 P m and subdivided grid graphs are odd harmonious.\",\"PeriodicalId\":36416,\"journal\":{\"name\":\"Cubo\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2020-12-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Cubo\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.4067/s0719-06462020000300299\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Cubo","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.4067/s0719-06462020000300299","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
摘要
如果存在注入f:V（G），则称图G（p，q）为奇调和图→ {0，1，2，··，2q−1}使得诱导函数f*:E（G）→ 由f＊（uv）=f（u）+f（v）定义的{1，3，···，2q−1}是双射。本文证明了T p-树◦ P m，T◦ 2 P m，普通竹子，C n◦ P m，C n◦ 2Pm和细分网格图是奇调和图。
A graph G ( p, q ) is said to be odd harmonious if there exists an injection f : V ( G ) → { 0 , 1 , 2 , · · · , 2 q − 1 } such that the induced function f ∗ : E ( G ) → { 1 , 3 , · · · , 2 q − 1 } defined by f ∗ ( uv ) = f ( u ) + f ( v ) is a bijection. In this paper we prove that T p - tree, T ˆ ◦ P m , T ˆ ◦ 2 P m , regular bamboo tree, C n ˆ ◦ P m , C n ˆ ◦ 2 P m and subdivided grid graphs are odd harmonious.
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