限制匹配数的k一致超树色熵极值

The Chromatic Entropy of a k-Uniform Hypertrees with Restricted Matching Number

摘要: 图熵被广泛地应用于表征图的系统结构的领域。图熵可以反映出图的不同的结构信息，还能反映出图的不同的复杂性度量。在物理，化学和医学等领域有着重要作用。超图作为普通图的一种推广，对于更加复杂的图结构能够更好的表现出关键信息，比如复杂网络等。自然而言，我们可以考虑将图熵推广到超图上，考虑基于超图的顶点染色的图熵，将超图顶点染色和图熵结合起来，得到更加复杂的色熵问题，为色熵问题在以后的研究中奠定了基础。本文主要研究了在限制最大匹配数的情况下，得到了k一致超树的色熵极值大小和极值图结构，并给出了相应的图。

Abstract: Graph entropy is widely applied in the field of characterizing the system structure of graphs. It can reflect different structural information and various complexity measures. It plays an important role in physics, chemistry, medicine and other fields. As a generalization of ordinary graphs, hypergraphs can better represent key information for more complex graph structures, such as complex networks. Naturally, we can consider extending graph entropy to hypergraphs, and consider the graph entropy based on vertex coloring of hypergraphs, combining hypergraph vertex coloring and graph entropy to obtain more complex chromatic entropy problems, providing a more long-term problem for chromatic entropy problems. This paper mainly studies the extremal values and extremal graph structures of chromatic entropy of k-uniform hypertrees under the condition of fixed maximum matching number, and gives the corresponding graphs.