论文标题
凯门尼在树上的恒定和维纳索引
Kemeny's constant and Wiener index on trees
论文作者
论文摘要
在固定秩序的树上，我们显示了凯门尼的常数和维也纳索引之间的直接关系，并通过组合解释从关系中提供了凯门尼常数的新公式。此外，这种关系简化了凯门尼（Kemeny）在树上随机行走的常数方面的几个已知结果证明。最后，我们为Co-Kemeny的伴侣提供了各种家族，它们是两个具有相同Kemeny常数的非同形连接图，我们还为树提供了必要的条件，以达到固定直径的树木的最大凯梅尼的常数。
On trees of fixed order, we show a direct relation between Kemeny's constant and Wiener index, and provide a new formula of Kemeny's constant from the relation with a combinatorial interpretation. Moreover, the relation simplifies proofs of several known results for extremal trees in terms of Kemeny's constant for random walks on trees. Finally, we provide various families of co-Kemeny's mates, which are two non-isomorphic connected graphs with the same Kemeny's constant, and we also give a necessary condition for a tree to attain maximum Kemeny's constant for trees with fixed diameter.
