A labeling of a graph G is a bijection from E（G） to the set {1,2,…,｜E （G）｜ }.A labeling is antimagic if for any distinct vertices x and y,the sum of the labels on edges incident to x is different from the sum o...A labeling of a graph G is a bijection from E（G） to the set {1,2,…,｜E （G）｜ }.A labeling is antimagic if for any distinct vertices x and y,the sum of the labels on edges incident to x is different from the sum of the labels on edges incident to y.We say that a graph is antimagic if it has an antimagic labeling.Hartsfield and Ringel conjectured in 1990 that every graph other than 2 K is antimagic.In this paper,we show that the antimagic conjecture is false for the case of disconnected graphs.Furthermore,we find some classes of disconnected graphs that are antimagic and some classes of graphs whose complement are disconnected are antimagic.展开更多
A labelingfof a graph G is a bijection from its edge set E（G） to the set {1,2,...,｜E（G）｜}, which is antimagic if for any distinct vertices x and y, the sum of the labels on edges incident to x is different from ...A labelingfof a graph G is a bijection from its edge set E（G） to the set {1,2,...,｜E（G）｜}, which is antimagic if for any distinct vertices x and y, the sum of the labels on edges incident to x is different from the sum of the labels on edges incident to y. A graph G is antimagic if G has anfwhich is antimagic. Hartsfield and Ringel conjectured in 1990 that every connected graph other than K2 is antimagic. In this paper, we show that if G1 is an m-vertex graph with maximum degree at most 6r＋ 1, and G2 is an n-vertex （2r）-regular graph （m≥n≥3）, then the join graph G1 v G2 is antimagic.展开更多
A labeling f of a graph G is a bijection from its edge set E（G） to the set {1, 2,……, E（G） }, which is antimagic if for any distinct vertices x and y, the sum of the labels on edges incident to x is different fro...A labeling f of a graph G is a bijection from its edge set E（G） to the set {1, 2,……, E（G） }, which is antimagic if for any distinct vertices x and y, the sum of the labels on edges incident to x is different from the sum of the labels on edges incident to y. A graph G is antimagic if G has an f which is antimagic. Hartsfield and Ringel conjectured in 1990 that every connected graph other than 2K is antimagic. In this paper, we show that some graphs with even factors are antimagic, which generalizes some known results.展开更多
A labeling f of a graph G is a bijection from its edge set E（G） to the set {1, 2, ..., ｜E（G）｜}, which is antimagic if for any distinct vertices x and y, the sum of the labels on edges incident to x is different ...A labeling f of a graph G is a bijection from its edge set E（G） to the set {1, 2, ..., ｜E（G）｜}, which is antimagic if for any distinct vertices x and y, the sum of the labels on edges incident to x is different from the sum of the labels on edges incident to y. A graph G is antimagic if G has an f which is antimagic. Hartsfield and Ringel conjectured in 1990 that every connected graph other than K2 is antimagic. In this paper, we show that if G1 is an n-vertex graph with minimum degree at least r, and G2 is an m-vertex graph with maximum degree at most 2r - 1 （m ≥ n）, then G1 V G2 is antimagic.展开更多
An antimagic labeling of a graph withq edges is a bijection from the set of edges to the set of positive integers{1,2,...,q}such that all vertex weights are pairwise distinct,where the vertex weight of a vertex is the...An antimagic labeling of a graph withq edges is a bijection from the set of edges to the set of positive integers{1,2,...,q}such that all vertex weights are pairwise distinct,where the vertex weight of a vertex is the sum of the labels of all edges incident with that vertex.A graph is antimagic if it has an antimagic labeling.In this paper,we provide antimagic labelings for a family of generalized pyramid graphs.展开更多
Hartsfield and Ringel conjectured that every connected graph other than K2 is antimagic.Since then,many classes of graphs have been proved to be antimagic.But few is known about the antimagicness of lexicographic prod...Hartsfield and Ringel conjectured that every connected graph other than K2 is antimagic.Since then,many classes of graphs have been proved to be antimagic.But few is known about the antimagicness of lexicographic product graphs.In this paper,via the construction of a directed Eulerian circuit,the Siamese method,and some modification on graph labeling,the antimagicness of lexicographic product graph G[Pn]is obtained.展开更多
Given a graph G with n vertices and an Abelian group A of order n, an A-distance antimagic labelling of G is a bijection from V（G） to A such that the vertices of G have pairwise distinct weights, where the weight of...Given a graph G with n vertices and an Abelian group A of order n, an A-distance antimagic labelling of G is a bijection from V（G） to A such that the vertices of G have pairwise distinct weights, where the weight of a vertex is the sum （under the operation of A） of the labels assigned to its neighbours. An A-distance magic labelling of G is a bijection from V（G） to A such that the weights of all vertices of G are equal to the same element of A. In this paper we study these new labellings under a general setting with a focus on product graphs. We prove among other things several general results on group antimagic or magic labellings for Cartesian, direct and strong products of graphs. As applications we obtain several families of graphs admitting group distance antimagic or magic labellings with respect to elementary Abelian groups, cyclic groups or direct products of such groups.展开更多
An m×k matrix is said to be a d-row(column)antimagic matrix if its row-sums(column-sums)form an arithmetic progression with a difference d.The goal of this paper is to obtain the existence theorems and constructi...An m×k matrix is said to be a d-row(column)antimagic matrix if its row-sums(column-sums)form an arithmetic progression with a difference d.The goal of this paper is to obtain the existence theorems and construction methods of some d-row(column)antimagic matrices.Using these results we give the necessary and sufficient condition for the existence of an(m,d)-partition of[1,mk].展开更多
基金Supported by the National Natural Science Foundation of China (10201022,10971144,and 11101020)the Natural Science Foundation of Beijing (1102015)the Fundamental Research Funds for the Central Universities(2011B019)
文摘A labeling of a graph G is a bijection from E（G） to the set {1,2,…,｜E （G）｜ }.A labeling is antimagic if for any distinct vertices x and y,the sum of the labels on edges incident to x is different from the sum of the labels on edges incident to y.We say that a graph is antimagic if it has an antimagic labeling.Hartsfield and Ringel conjectured in 1990 that every graph other than 2 K is antimagic.In this paper,we show that the antimagic conjecture is false for the case of disconnected graphs.Furthermore,we find some classes of disconnected graphs that are antimagic and some classes of graphs whose complement are disconnected are antimagic.
基金Supported by the National Natural Science Foundation of China(11371052,11271267,10971144,11101020)the Natural Science Foundation of Beijing(1102015)the Fundamental Research Funds for the Central Univer sities(2011B019,3142013104)
文摘A labelingfof a graph G is a bijection from its edge set E（G） to the set {1,2,...,｜E（G）｜}, which is antimagic if for any distinct vertices x and y, the sum of the labels on edges incident to x is different from the sum of the labels on edges incident to y. A graph G is antimagic if G has anfwhich is antimagic. Hartsfield and Ringel conjectured in 1990 that every connected graph other than K2 is antimagic. In this paper, we show that if G1 is an m-vertex graph with maximum degree at most 6r＋ 1, and G2 is an n-vertex （2r）-regular graph （m≥n≥3）, then the join graph G1 v G2 is antimagic.
基金Supported by the National Natural Science Foundation of China(11371052,11271267,10971144,11101020)the Fundamental Research Fund for the Central Universities(2011B019,3142013104,3142014127 and 3142014037)the North China Institute of Science and Technology Key Discipline Items of Basic Construction(HKXJZD201402)
文摘A labeling f of a graph G is a bijection from its edge set E（G） to the set {1, 2,……, E（G） }, which is antimagic if for any distinct vertices x and y, the sum of the labels on edges incident to x is different from the sum of the labels on edges incident to y. A graph G is antimagic if G has an f which is antimagic. Hartsfield and Ringel conjectured in 1990 that every connected graph other than 2K is antimagic. In this paper, we show that some graphs with even factors are antimagic, which generalizes some known results.
基金Supported by Fundamental Research Funds for the Central Universities(Grant No.2011B019)National Natural Science Foundation of China(Grant Nos.11101020,11171026,10201022and10971144) Natural Science Foundation of Beijing(Grant No.1102015)
文摘A labeling f of a graph G is a bijection from its edge set E（G） to the set {1, 2, ..., ｜E（G）｜}, which is antimagic if for any distinct vertices x and y, the sum of the labels on edges incident to x is different from the sum of the labels on edges incident to y. A graph G is antimagic if G has an f which is antimagic. Hartsfield and Ringel conjectured in 1990 that every connected graph other than K2 is antimagic. In this paper, we show that if G1 is an n-vertex graph with minimum degree at least r, and G2 is an m-vertex graph with maximum degree at most 2r - 1 （m ≥ n）, then G1 V G2 is antimagic.
文摘An antimagic labeling of a graph withq edges is a bijection from the set of edges to the set of positive integers{1,2,...,q}such that all vertex weights are pairwise distinct,where the vertex weight of a vertex is the sum of the labels of all edges incident with that vertex.A graph is antimagic if it has an antimagic labeling.In this paper,we provide antimagic labelings for a family of generalized pyramid graphs.
基金supported by the National Natural Science Foundation of China (Nos. 11401430)
文摘Hartsfield and Ringel conjectured that every connected graph other than K2 is antimagic.Since then,many classes of graphs have been proved to be antimagic.But few is known about the antimagicness of lexicographic product graphs.In this paper,via the construction of a directed Eulerian circuit,the Siamese method,and some modification on graph labeling,the antimagicness of lexicographic product graph G[Pn]is obtained.
基金Cichacz was partially supported by the Polish Ministry of Science and Higher EducationZhou was supported by the Australian Research Council(FT110100629)
文摘Given a graph G with n vertices and an Abelian group A of order n, an A-distance antimagic labelling of G is a bijection from V（G） to A such that the vertices of G have pairwise distinct weights, where the weight of a vertex is the sum （under the operation of A） of the labels assigned to its neighbours. An A-distance magic labelling of G is a bijection from V（G） to A such that the weights of all vertices of G are equal to the same element of A. In this paper we study these new labellings under a general setting with a focus on product graphs. We prove among other things several general results on group antimagic or magic labellings for Cartesian, direct and strong products of graphs. As applications we obtain several families of graphs admitting group distance antimagic or magic labellings with respect to elementary Abelian groups, cyclic groups or direct products of such groups.
基金supported by the National Natural Science Foundation of China(No.11871190)。
文摘An m×k matrix is said to be a d-row(column)antimagic matrix if its row-sums(column-sums)form an arithmetic progression with a difference d.The goal of this paper is to obtain the existence theorems and construction methods of some d-row(column)antimagic matrices.Using these results we give the necessary and sufficient condition for the existence of an(m,d)-partition of[1,mk].
