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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References
Bian Q (2010) Generalization of fractional matching extensions in graphs. Math Pract Theory 40(9):173–179
Chiclana F, Mata F, Pérez LG et al (2018) Type-1 OWA unbalanced fuzzy linguistic aggregation methodology: application to eurobonds credit risk evaluation. Int J Intell Syst 33:1071–1088
Espada JP, Garca-Daz V, Núñez-Valdéz ER et al (2019) Real-time force doors detection system using distributed sensors and neural networks. Int J Intell Syst 34(9):2243–2252
Gao W (2012) Some results on fractional deleted graphs. Doctoral disdertation of Soochow university
Gao W, Wang W (2014) Binding number and fractional \((g, f, n^{\prime }, m)\)-critical deleted graph. Ars Combinatoria 113A:49–64
Gao W, Zhang Y, Chen Y (2018) Neighborhood condition for all fractional \((g, f, n^{\prime }, m)\)-critical deleted graphs. Open Phys. 16:544–553
Gao W, Guirao JLG, Chen Y (2019a) A toughness condition for fractional \((k, m)\)-deleted graphs revisited. Acta Mathematica Sinica Engl Ser 35(7):1227–1237
Gao W, Wang W, Dimitrov D (2019b) Toughness condition for a graph to be all fractional \((g, f, n)\)-critical deleted. Filomat 33(9):2735–2746
Hu B, Wang H, Yu X et al (2019) Sparse network embedding for community detection and sign prediction in signed social networks. J Ambient Intell Humaniz Comput 10:175–186
Li Z, Yan G (2004) Some result on the graphic isolated toughness and the existence of fractional factor. Acta Mathematicae Applicatae Sinica 27(2):324–333
Li J, Yan H, Liu Z et al (2017) Location-sharing systems with enhanced privacy in mobile online social networks. IEEE Syst J 11:439–448
Li J, Sun L, Yan Q et al (2018) Significant permission identification for machine-learning-based android malware detection. IEEE Trans Ind Inf 14:3216–3225
Liu G, Zhang L (2008) Toughness and the existence of fractional \(k\)-factors of graphs. Discrete Math 308:1741–1748
Ma Y, Liu G (2004) Some results on fractional \(k\)-extendable graphs. Chin J Eng Math 21(4):567–573
Malik H, Yasar A, Shakshuki EM (2019) Towards augmenting ambient systems networks and technologies. J Ambient Intell Humaniz Comput 10:2493–2494
Muneeza Abdullah S, Aslam M (2020) New multicriteria group decision support systems for small hydropower plant locations selection based on intuitionistic cubic fuzzy aggregation information. Int J Intell Syst. https://doi.org/10.1002/int.22233
Woodall D (1973) The binding number of a graph and its Anderson number. J Comb Theory Ser B 15:225–255
Yang J, Ma Y, Liu G (2001) Fractional \((g, f)\)-factors in graphs. Appl Math J Chin Univ Ser A 16:385–390
Zhang L, Liu G (2001) Fractional \(k\)-factor of graphs. J Syst Sci Math Sci 21(1):88–92
Zhou S (2020) Remarks on path factors in graphs. RAIRO Oper Res. https://doi.org/10.1051/ro/2019111
Zhou S, Sun Z (2020a) Binding number conditions for \(P_{\ge 2}\)-factor and \(P_{\ge 3}\)-factor uniform graphs. Discrete Math 343(3):111715
Zhou S, Sun Z (2020b) Some existence theorems on path factors with given properties in graphs. Acta Mathematica Sinica Engl Ser. https://doi.org/10.1007/s10114-020-9224-5
Zhou S, Xu Y, Sun Z (2019) Degree conditions for fractional \((a, b, k)\)-critical covered graphs. Inf Process Lett 152:105838
Zhou S, Liu H, Xu Y (2020a) Binding numbers for fractional \((a, b, k)\)-critical covered graphs. Proc Rom Acad Ser A Math Phys Tech Sci Inf Sci 21(2):115–121
Zhou S, Zhang T, Xu Z (2020b) Subgraphs with orthogonal factorizations in graphs. Discrete Appl Math. https://doi.org/10.1016/j.dam.2019.12.011
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This work is supported by NSFC (no. 11761083).
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Gao, W., Yan, L., Li, Y. et al. Network performance analysis from binding number prospect. J Ambient Intell Human Comput 13, 1259–1267 (2022). https://doi.org/10.1007/s12652-020-02553-3
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DOI: https://doi.org/10.1007/s12652-020-02553-3