Vertex-antimagic Labelings of Regular Graphs

作     者：Ali AHMAD Kashif ALI Martin BACA Petr KOVAR Andrea SEMANICOVA-FENOVCíKOVA Ali AHMAD;Kashif ALI;Martin BA(C)A;Petr KOV(A)(R);Andrea SEMANI(C)OV(A)-FE(N)OV(C)(I)KOV(A)

作者机构：College of Computer Science and Information SystemsJazan University Faculty of MathematicsCOMSATS Institute of Information Technology Department of Applied Mathematics and InformaticsTechnical University Department of Applied MathematicsVB-Technical University of Ostrava 

出 版 物：《Acta Mathematica Sinica,English Series》 (数学学报（英文版）)

年 卷 期：2012年第28卷第9期

页      面：1865-1874页

核心收录：

学科分类：07[理学] 08[工学] 070104[理学-应用数学] 0701[理学-数学] 081202[工学-计算机软件与理论] 0812[工学-计算机科学与技术（可授工学、理学学位）] 

基　　金：Supported by Slovak VEGA Grant 1/0130/12 Higher Education Commission Pakistan (Grant No.HEC(FD)/2007/555) the Ministry of Education of the Czech Republic (Grant No. MSM6198910027) 

主　　题：Super vertex-antimagic total labeling vertex-antimagic edge labeling regular graph 

摘      要：Let G = （V, E） be a finite, simple and undirected graph with p vertices and q edges. An （a, d）-vertex-antimagic total labeling of G is a bijection f from V（G） t2 E（G） onto the set of consecutive integers 1, 2,... ,p ＋ q, such that the vertex-weights form an arithmetic progression with the initial term a and difference d, where the vertex-weight of x is the sum of the value f（x） assigned to the vertex x together with all values f（xy） assigned to edges xy incident to x. Such labeling is called super if the smallest possible labels appear on the vertices. In this paper, we study the properties of such labelings and examine their existence for 2r-regular graphs when the difference d is 0, 1,..., r ＋ 1.