{"title":"Pn⊵C4和Pn⊵D2(C4)的奇调和标记","authors":"Sabrina Shena Sarasvati, Ikhsanul Halikin, Kristiana Wijaya","doi":"10.19184/ijc.2021.5.2.5","DOIUrl":null,"url":null,"abstract":"A graph <em>G</em> with <em>q</em> edges is said to be odd harmonious if there exists an injection <em>f</em>:<em>V</em>(<em>G</em>) → ℤ<sub>2q</sub> so that the induced function <em>f</em>*:<em>E</em>(<em>G</em>)→ {1,3,...,2<em>q</em>-1} defined by <em>f</em>*(<em>uv</em>)=<em>f</em>(<em>u</em>)+<em>f</em>(<em>v</em>) is a bijection.<p>Here we show that graphs constructed by edge comb product of path <em>P</em><sub>n</sub> and cycle on four vertices <em>C</em><sub>4</sub> or shadow of cycle of order four <em>D</em><sub>2</sub>(<em>C</em><sub>4</sub>) are odd harmonious.</p>","PeriodicalId":13506,"journal":{"name":"Indonesian Journal of Combinatorics","volume":"58 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2021-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Odd Harmonious Labeling of <em>P</em><sub>n</sub> ⊵ <em>C</em><sub>4 </sub>and <em>P</em><sub>n</sub> ⊵ <em>D</em><sub>2</sub>(<em>C</em><sub>4</sub>)\",\"authors\":\"Sabrina Shena Sarasvati, Ikhsanul Halikin, Kristiana Wijaya\",\"doi\":\"10.19184/ijc.2021.5.2.5\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"A graph <em>G</em> with <em>q</em> edges is said to be odd harmonious if there exists an injection <em>f</em>:<em>V</em>(<em>G</em>) → ℤ<sub>2q</sub> so that the induced function <em>f</em>*:<em>E</em>(<em>G</em>)→ {1,3,...,2<em>q</em>-1} defined by <em>f</em>*(<em>uv</em>)=<em>f</em>(<em>u</em>)+<em>f</em>(<em>v</em>) is a bijection.<p>Here we show that graphs constructed by edge comb product of path <em>P</em><sub>n</sub> and cycle on four vertices <em>C</em><sub>4</sub> or shadow of cycle of order four <em>D</em><sub>2</sub>(<em>C</em><sub>4</sub>) are odd harmonious.</p>\",\"PeriodicalId\":13506,\"journal\":{\"name\":\"Indonesian Journal of Combinatorics\",\"volume\":\"58 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2021-12-28\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Indonesian Journal of Combinatorics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.19184/ijc.2021.5.2.5\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Indonesian Journal of Combinatorics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.19184/ijc.2021.5.2.5","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Odd Harmonious Labeling of Pn ⊵ C4 and Pn ⊵ D2(C4)
A graph G with q edges is said to be odd harmonious if there exists an injection f:V(G) → ℤ2q so that the induced function f*:E(G)→ {1,3,...,2q-1} defined by f*(uv)=f(u)+f(v) is a bijection.
Here we show that graphs constructed by edge comb product of path Pn and cycle on four vertices C4 or shadow of cycle of order four D2(C4) are odd harmonious.
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