The Hosoya polynomial is a well known vertex-distance based polynomial,closely correlated to the Wiener index and the hyper-Wiener index, which arewidely used molecular-structure descriptors. In the present paper we considerthe edge version of the Hosoya polynomial. For a connected graph $G$ let$d_e(G,k)$ be the number of (unordered) edge pairs at distance $k$. Then theedge-Hosoya polynomial of $G$ is $H_e(G,x) = \sum_{k \geq 0} d(G,k)x^k$. Weinvestigate the edge-Hosoya polynomial of important chemical graphs known asbenzenoid chains and derive the recurrence relations for them. Theserecurrences are then solved for linear benzenoid chains, which are also calledpolyacenes.
展开▼
机译：Hosoya多项式是一个众所周知的基于顶点距离的多项式，与广泛使用的分子结构描述符Wiener指数和hyper-Wiener指数密切相关。在本文中，我们考虑了Hosoya多项式的边沿版本。对于一个连通图$ G $，令$ d_e（G，k）$为距离$ k $的（无序）边对的数量。则$ G $的edge-Hosoya多项式为$ H_e（G，x）= \ sum_ {k \ geq 0} d（G，k）x ^ k $。我们研究了重要化学图的边Hosoya多项式，称为苯系链，并推导了它们的递归关系。然后，针对线性的类苯环链（也称为聚苯乙炔）求解这些递归。
展开▼
