{"title":"几类图的超(a,d)边反幻全标记","authors":"P. R. L. Pushpam, A. Saibulla","doi":"10.55937/sut/1343931268","DOIUrl":null,"url":null,"abstract":"A graph G(V, E) is (a, d)-edge antimagic total if there exists a bijection f : V (G) ∪ E(G) → {1, 2, . . . , |V (G)| + |E(G)|} such that the edge- weights Λ(uv) = f (u)+f (uv)+f (v), uv ∈ E(G) form an arithmetic progression with first term a and common difference d. It is said to be a super (a, d)-edge antimagic total if f (V (G)) = {1, 2, . . . , |V (G)|}. In this paper, we have obtained a relation between a super (a, 0)-edge antimagic total labeling and a super (a, 2)- edge antimagic total labeling of any graph. Also we study the super (a, d)-edge antimagic total labeling of fan graphs and two special classes of star graphs namely bi-star and extended bi-star. AMS 2010 Mathematics Subject Classification. 05C78.","PeriodicalId":38708,"journal":{"name":"SUT Journal of Mathematics","volume":"16 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2012-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"9","resultStr":"{\"title\":\"Super (a,d)-edge antimagic total labeling of some classes of graphs\",\"authors\":\"P. R. L. Pushpam, A. Saibulla\",\"doi\":\"10.55937/sut/1343931268\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"A graph G(V, E) is (a, d)-edge antimagic total if there exists a bijection f : V (G) ∪ E(G) → {1, 2, . . . , |V (G)| + |E(G)|} such that the edge- weights Λ(uv) = f (u)+f (uv)+f (v), uv ∈ E(G) form an arithmetic progression with first term a and common difference d. It is said to be a super (a, d)-edge antimagic total if f (V (G)) = {1, 2, . . . , |V (G)|}. In this paper, we have obtained a relation between a super (a, 0)-edge antimagic total labeling and a super (a, 2)- edge antimagic total labeling of any graph. Also we study the super (a, d)-edge antimagic total labeling of fan graphs and two special classes of star graphs namely bi-star and extended bi-star. AMS 2010 Mathematics Subject Classification. 05C78.\",\"PeriodicalId\":38708,\"journal\":{\"name\":\"SUT Journal of Mathematics\",\"volume\":\"16 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2012-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"9\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"SUT Journal of Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.55937/sut/1343931268\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"SUT Journal of Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.55937/sut/1343931268","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"Mathematics","Score":null,"Total":0}
引用次数: 9
摘要
如果存在双射f: V (G)∪E(G)→{1,2，…，则图G(V, E)是(A, d)边反奇异全。， |V (G)| + |E(G)|}，使得边权Λ(uv) = f (u)+f (uv)+f (V)， uv∈E(G)形成第一项为a且公差为d的等差数列。若f (V (G)) ={1,2，…，则称其为超(a, d)边反奇异总数。， | v (g)|}。本文得到了任意图的超(a, 0)边反幻全标记与超(a, 2)边反幻全标记之间的关系。此外，我们还研究了扇形图的超(a, d)边反幻全标记，以及两类特殊的星图即双星和扩展双星。AMS 2010数学学科分类。05 5c78。
Super (a,d)-edge antimagic total labeling of some classes of graphs
A graph G(V, E) is (a, d)-edge antimagic total if there exists a bijection f : V (G) ∪ E(G) → {1, 2, . . . , |V (G)| + |E(G)|} such that the edge- weights Λ(uv) = f (u)+f (uv)+f (v), uv ∈ E(G) form an arithmetic progression with first term a and common difference d. It is said to be a super (a, d)-edge antimagic total if f (V (G)) = {1, 2, . . . , |V (G)|}. In this paper, we have obtained a relation between a super (a, 0)-edge antimagic total labeling and a super (a, 2)- edge antimagic total labeling of any graph. Also we study the super (a, d)-edge antimagic total labeling of fan graphs and two special classes of star graphs namely bi-star and extended bi-star. AMS 2010 Mathematics Subject Classification. 05C78.
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