Cycle-magic graphs
Cycle-magic graphs
复制标题
DOI：
10.1016/j.disc.2007.03.007
复制
发表时间：
2007-11-06
影响因子：
0.8
通讯作者：
Moragas, J.
中科院分区：
文献类型：
--
作者：
Llado, A.;Moragas, J.
一个简单图G =（V，E）允许圈覆盖，如果E中的每条边至少属于G的一个同构于给定圈C的子图.如果存在全标号f：Vboolean OR E -> {1，2，.，垂直线V垂直线+垂直线E垂直线}使得对于G的每个同构于C的子图H '=（V'，E '），Sigma（v <$V'）f（v）+ Sigma（e <$E '）f（e）是常数.当f（V）= {1，.，我们研究了几类连通图的圈幻和圈超幻行为。对于每个r >= 3，我们给出了几类C-r-幻图。结果依赖于一种技术的分区集的整数具有特殊性质。(C)2007 Elsevier B. V.保留所有权利。
A simple graph G = (V, E) admits a cycle-covering if every edge in E belongs at least to one subgraph of G isomorphic to a given cycle C. Then the graph G is C-magic if there exists a total labelling f : V boolean OR E -> {1, 2,..., vertical bar V vertical bar + vertical bar E vertical bar} such that, for every subgraph H'= (V', E') of G isomorphic to C, Sigma(v epsilon V') f (v) + Sigma(e epsilon E') f (e) is constant. When f (V) = {1,..., vertical bar V vertical bar}, then G is said to be C-supermagic.We study the cyclic-magic and cyclic-supermagic behavior of several classes of connected graphs. We give several families of C-r-magic graphs for each r >= 3. The results rely on a technique of partitioning sets of integers with special properties. (C) 2007 Elsevier B.V. All rights reserved.