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
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
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
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(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.
