A matching M of a graph G is an induced matching if no two edges in M are joined by an edge of G . Let iz ( G ) denote the total number of induced matchings of G , named iz -index. It is well known that the Hosoya index of a graph is the total number of matchings and the Hosoya index of a path can be calculated by the Fibonacci sequence. In this paper, we investigate the iz -index of graphs by using the Fibonacci-Narayana sequence and characterize some types of graphs with minimum and maximum iz -index, respectively.

中文翻译：

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图的诱导匹配数

图 G 的匹配 M 是诱导匹配，如果 M 中没有两条边由 G 的边连接。让 iz ( G ) 表示 G 的诱导匹配总数，命名为 iz -index。众所周知，图的细谷指数是匹配的总数，路径的细谷指数可以通过斐波那契数列来计算。在本文中，我们通过使用 Fibonacci-Narayana 序列来研究图的 iz-index，并分别用最小和最大 iz-index 来表征一些类型的图。