Abstract
As a parameter from the perspective of neighborhood structure in network, binding number is applied to measure the vulnerability of the network. The network is represented by a graph, and the binding number bind(G) can be expressed by minimizing the ratio $$|N_{G}(X)|:|X|$$ over all $$\emptyset \ne X\subseteq V(G)$$ which satisfying that the neighborhood of X in G is not equal to whole vertex set. The previous results show that bind(G) is closely related to the existence of fractional factor and matching in graphs which imply the feasibility of data transmission and task scheduling in the network. In our work, we investigate the relationship between fractional matching extendable and binding number in networks, as well as the inner connection between binding number and the fractional (g, f, n)-critical deleted graphs. In view of graph structure analysis and mathematical derivation, several sufficient conditions in various settings are given.
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