基于拉普拉斯度的k-均匀超图的图熵极值

Extremality of graph entropy based on Laplacian degrees of k-uniform hypergraphs

基于一般图中图熵的定义,定义了超图基于拉普拉斯度的图熵.将简单图的图熵的一些结论推广到k-均匀超图.利用一种移边操作,分别确定了在k-均匀超树、单圈k-均匀超图、双圈k-均匀超图和k-均匀化学超树中基于拉普拉斯度的图熵最大值和最小值,并确定了相应的极值图.

Motivated by the definition of graph entropy in general graphs,the graph entropy of hypergraphs based on Laplacian degree are defined.Some results on graph entropy of simple graphs are extended to k-uniform hypergraphs.By an operation of edge moving,the maximum and minimum graph entropy based on Laplacian degrees are determined in k-uniform hypertrees,unicyclic k-uniform hypergraphs,bicyclic k-uniform hypergraphs and k-uniform chemical hypertrees,respectively,and the corresponding extremal graphs are determined.