论文标题
Zykov的诊断数量等于其和谐数的挖掘额
Zykov sums of digraphs with diachromatic number equal to their harmonious number
论文作者
论文摘要
考虑到无环着色的二分法数量和惯用数字是色数的概括和挖掘的成本数字。在本文中，我们确定了由Zykov的Digraphs总和引起的杂交数量，这些挖掘物以$ k = \ tfrac {1+ \ sqrt {1+sqrt {1+4m}}} {2} {2} {合适的$ m $而言，$ k = \ tfrac {1+ \ sqrt {1+ \ sqrt {1+\ sqrt {1+ \ sqrt {1+ \ tfrac {1+\ sqrt {1+ \ tfrac）。因此，惯性数量等于这个家庭中每个挖掘的和谐数。特别是，我们研究了Zykov循环总和的色数，谈期和谐的色数。
The dichromatic number and the diachromatic number are generalizations of the chromatic number and the achromatic number for digraphs considering acyclic colorings. In this paper, we determine the diachromatic number of digraphs arising from the Zykov sum of digraphs that admit a complete $k$-coloring with $k=\tfrac{1+\sqrt{1+4m}}{2}$ for a suitable $m$. Consequently, the diachromatic number equals the harmonious number for every digraph in this family. In particular, we study the chromatic number, the diachromatic number, and the harmonious chromatic number of the Zykov sum of cycles.
