论文标题
两分图的基于学位的熵的极值
Extremal values of degree-based entropies of bipartite graphs
论文作者
论文摘要
我们表征了将（基于一级的）熵（在给定尺寸的所有两部分图）或给定尺寸和（上限上）的两部分熵最小化的两部分图。极端图结果是完整的两部分图，或几乎完整的两部分。在这里，我们利用Young tableaux使用两分图的等效表示，这使比较相关图的熵变得更加容易。我们得出的结论是，由于它与数字理论的联系，因此极端图的一般表征是一个困难的问题，但是对于$ n $和大小$ m $的特定值，它们很容易找到。我们还提供了一个直接的参数来表征最大化给定顺序和大小的熵的图形。我们表明，我们的一些想法也扩展到其他基于学位的拓扑指数。
We characterize the bipartite graphs that minimize the (first-degree based) entropy, among all bipartite graphs of given size, or given size and (upper bound on the) order. The extremal graphs turn out to be complete bipartite graphs, or nearly complete bipartite. Here we make use of an equivalent representation of bipartite graphs by means of Young tableaux, which make it easier to compare the entropy of related graphs. We conclude that the general characterization of the extremal graphs is a difficult problem, due to its connections with number theory, but they are easy to find for specific values of the order $n$ and size $m$. We also give a direct argument to characterize the graphs maximizing the entropy given order and size. We indicate that some of our ideas extend to other degree-based topological indices as well.
