论文标题
（边缘）电晕和分层产品的主导和统治者着色
Dominated and dominator colorings over (edge) corona and hierarchical products
论文作者
论文摘要
图形的统治者着色是一种适当的（顶点）着色，其属性是每个顶点单独的颜色类别，或者与至少一个颜色类的所有顶点相邻。图形的主导着色是适当的着色，因此每个颜色类都以至少一个顶点为主。确定了电晕产品和边缘电晕产品的统治者色数。为主导数量的边缘电晕产品提供了尖锐的下限和上限。层次产物的统治者色数从上方界定，并以两个因素确定的层次结构产物数。还提出了在遗传网络中主导的着色的应用。
Dominator coloring of a graph is a proper (vertex) coloring with the property that every vertex is either alone in its color class or adjacent to all vertices of at least one color class. A dominated coloring of a graph is a proper coloring such that every color class is dominated with at least one vertex. The dominator chromatic number of corona products and of edge corona products is determined. Sharp lower and upper bounds are given for the dominated chromatic number of edge corona products. The dominator chromatic number of hierarchical products is bounded from above and the dominated chromatic number of hierarchical products with two factors determined. An application of dominated colorings in genetic networks is also proposed.
