A Radio Coloring of a Hypercube
A Radio Coloring of a Hypercube
复制标题
超立方体的无线电着色
DOI：
10.1080/00207160211287
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发表时间：
2002
影响因子：
1.8
通讯作者：
P. Wan
中科院分区：
文献类型：
--
作者：
O. Frieder;F. Harary;P. Wan
图G的一个无线电着色是指给它的节点分配非负整数，使得每对相邻节点的色数至少相差2，并且距离为2的任何一对节点都有不同的颜色。每个图都有一个无线电着色，只需分配奇数1，3，5，@，但最小和最大的颜色之间有很大的差异。我们定义G的一个无线电着色的跨度为1加上最小和最大颜色之间的差。本文研究超立方体的射电染色，目的是找到具有最小跨度的射电染色。我们开发一个配方，我们认为是这个问题的完整解决方案的形式的猜想。
A radio coloring of a graph G is an assignment of nonnegative integers to its nodes so that each pair of adjacent nodes have color numbers that differ by at least two, and any pair of nodes at distance 2 have different colors. Every graph has a radio coloring by simply assigning the odd integers 1,3, 5, @, but there is then a big difference between the smallest and largest colors. We define the span of a radio coloring of G as one plus the difference between the smallest and largest colors. We study radio colorings of a hypercube with the objective of finding such a coloring with minimum span. We develop a formulation for what we believe is the complete solution to this question in the form of a conjecture.