Abstract
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.
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This work is supported by the Science and Technology Program of Guangzhou, China (No.202002030183), by the Qinghai Province Natural Science Foundation (No.2020-ZJ-924) and by the Guangdong Province Natural Science Foundationauthorized in 2020).
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Chen, Y., Liu, Y. Number of Induced Matchings of Graphs. Acta Math. Appl. Sin. Engl. Ser. 37, 35–47 (2021). https://doi.org/10.1007/s10255-021-0996-x
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DOI: https://doi.org/10.1007/s10255-021-0996-x