The matching preclusion number of a graph is the minimum number of edges whose deletion results in a graph that has neither perfect matchings nor almost perfect matchings. As a generalization, Liu and Liu  recently introduced the concept of fractional matching preclusion number. The fractional matching preclusion number (FMP number) of G, denoted by fmp(G), is the minimum number of edges whose deletion leaves the resulting graph without a fractional perfect matching. The fractional strong matching preclusion number (FSMP number) of G, denoted by fsmp(G), is the minimum number of vertices and edges whose deletion leaves the resulting graph without a fractional perfect matching. In this paper, we study the fractional matching preclusion number and the fractional strong matching preclusion number for butterfly network, augmented butterfly network and enhanced butterfly network.
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Wang, Xia; Ma, Tianlong; Ye, Chengfu; Xiao, Yuzhi; and Wang, Fang
"Fractional matching preclusion for butterfly derived networks,"
Theory and Applications of Graphs: Vol. 6
, Article 3.
Available at: https://digitalcommons.georgiasouthern.edu/tag/vol6/iss1/3