A Note of Generalization of Fractional ID-factor-critical Graphs

• Autorzy: Sizhong Zhou

Identyfikatory

DOI

10.3233/FI-222130

• Języki publikacji: EN

Abstrakty

EN

In communication networks, the binding numbers of graphs (or networks) are often used to measure the vulnerability and robustness of graphs (or networks). Furthermore, the frac- tional factors of graphs and the fractional ID-[a, b]-factor-critical covered graphs have a great deal of important applications in the data transmission networks. In this paper, we investigate the rela- tionship between the binding numbers of graphs and the fractional ID-[a, b]-factor-critical covered graphs, and derive a binding number condition for a graph to be fractional ID-[a, b]-factor-critical covered, which is an extension of Zhou’s previous result [S. Zhou, Binding numbers for fractional ID-k-factor-critical graphs, Acta Mathematica Sinica, English Series 30(1)(2014)181–186].

Słowa kluczowe

EN

network, graph; binding number; fractional [a, b]-factor; fractional ID-[a, b]-factor-critical covered graph

• Wydawca: IOS Press
• Czasopismo: Fundamenta Informaticae
• Rocznik: 2022
• Tom: Vol. 187 nr 1
• Strony: 61--69
• Opis fizyczny: Bibliogr. 31 poz.

Twórcy

autor

Sizhong Zhou

• School of Science Jiangsu University of Science and Technology Zhenjiang, Jiangsu 212100, China

Bibliografia

• [1] Araujo DRB, Martins JF, Bastos CJA. New graph model to design optical networks. IEEE Communications Letters, 2015. 19(12):2130-2133. doi:10.1109/LCOMM.2015.2480716.
• [2] Ashwin P, Postlethwaite C. On designing heteroclinic networks from graphs. Physica D, 2013. 265:26-39. doi:10.1016/j.physd.2013.09.006.
• [3] Bauer D, Nevo A, Schmeichel E. Best monotone degree condition for the Hamiltonicity of graphs with a 2-factor. Graphs and Combinatorics, 2017. 33(5):1231-1248. doi:10.1007/s00373-017-1840-1.
• [4] Fardad M, Lin F, Jovanovic MR. Design of optimal sparse interconnection graphs for synchronization of oscillator networks. IEEE Transactions on Automatic Control, 2014. 59(9):2457-2462. doi:10.1109/TAC. 2014.2301577.
• [5] Gao W, Guirao J, Wu H. Two tight independent set conditions for fractional (g, f, m)-deleted graphs systems. Qualitative Theory of Dynamical Systems, 2018. 17(1):231-243. doi:10.1007/s12346-016-0222-z.
• [6] Gao W, Guirao J, Chen Y. A toughness condition for fractional (k, m)-deleted graphs revisited. Acta Mathematica Sinica, English Series, 2019. 35(7):1227-1237. doi:10.1007/s10114-019-8169-z.
• [7] Gao W, Wang W, Dimitrov D. Toughness condition for a graph to be all fractional (g, f, n)-critical deleted. Filomat, 2019. 33(9):2735-2746. doi:10.2298/FIL1909735G.
• [8] Haghparast N, Kiani D. Edge-connectivity and edges of even factors of graphs. Discussiones Mathematicae Graph Theory, 2019. 39(2):357-364. doi:10.7151/dmgt.2082.
• [9] Hasanvand M. Factors and connected factors in tough graphs with high isolated toughness. Dec. 30. arXiv: 1812.11640, 2018. doi:10.48550/arXiv.1812.11640.
• [10] Jiang J. A sufficient condition for all fractional [a, b]-factors in graphs. Proceedings of the Romanian Academy, Series A, 2018. 19(2):315-319.
• [11] Lanzeni S, Messina E, Archetti F. Graph models and mathematical programming in biochemical network analysis and metabolic engineering design. Computers and Mathematics with Applications, 2008. 55(5):970-983. doi:10.1016/j.camwa.2006.12.101.
• [12] Li Z, Yan G, Zhang X. On fractional (g, f )-covered graphs. OR Transactions (China), 2002. 6(4):65-68.
• [13] Pishvaee MS, Rabbani M. A graph theoretic-based heuristic algorithm for responsive supply chain network design with direct and indirect shipment. Advances in Engineering Software, 2011. 42(3):57-63. doi:10.1016/j.advengsoft.2010.11.001.
• [14] Rahimi M, Haghighi A. A graph portioning approach for hydraulic analysis-design of looped pipe networks. Water Resources Management, 2015. 29(14):5339-5352. doi:10.1007/s11269-015-1121-9.
• [15] Sun Z, Zhou S. A generalization of orthogonal factorizations in digraphs. Information Processing Letters, 2018. 132:49-54. doi:10.1016/j.ipl.2017.12.003.
• [16] Woodall DR. The binding number of a graph and its Anderson number. Journal of Combinatorial Theory, Series B, 1973. 15(3):225-255. doi:10.1016/0095-8956(73)90038-5.
• [17] Wang S, Zhang W. Isolated toughness for path factors in networks. RAIRO-Operations Research, 2022. 56(4):2613-2619. doi:10.1051/ro/2022123.
• [18] Wang S, Zhang W. On k-orthogonal factorizations in networks. RAIRO-Operations Research, 2021. 55(2):969-977. doi:10.1051/ro/2021037.
• [19] Wang S, Zhang W. Research on fractional critical covered graphs. Problems of Information Transmission, 2020. 56(3):270-277. doi:10.1134/S0032946020030047.
• [20] Zhou S. A neighborhood union condition for fractional (a, b, k)-critical covered graphs. Discrete Applied Mathematics, 2021. doi:10.1016/j.dam.2021.05.022.
• [21] Zhou S. A result on fractional (a, b, k)-critical covered graphs. Acta Mathematicae Applicatae Sinica-English Series, 2021. 37(4):657-664. doi:10.1007/s10255-021-1034-8.
• [22] Zhou S. Binding numbers for fractional ID-k-factor-critical graphs. Acta Mathematica Sinica, English Series, 2014. 30(1):181-186. doi:10.1007/s10114-013-1396-9.
• [23] Zhou S. Remarks on restricted fractional (g, f )-factors in graphs. Discrete Applied Mathematics, 2022. doi:10.1016/j.dam.2022.07.020.
• [24] Zhou S, Bian Q. The existence of path-factor uniform graphs with large connectivity. RAIRO-Operations Research, 2022. doi:10.1051/ro/2022143.
• [25] Zhou S, Bian Q, Pan Q. Path factors in subgraphs. Discrete Applied Mathematics, 2022. 319:183-191. doi:10.1016/j.dam.2021.04.012.
• [26] Zhou S, Liu H. Discussions on orthogonal factorizations in digraphs. Acta Mathematicae Applicatae Sinica-English Series, 2022. 38(2):417-425. doi:10.1007/s10255-022-1086-4.
• [27] Zhou S, Liu H, Xu Y. A note on fractional ID-[a, b]-factor-critical covered graphs. Discrete Applied Mathematics, 2022. 319:511-516. doi:10.1016/j.dam.2021.03.004.
• [28] Zhou S, Sun Z, Bian Q. Isolated toughness and path-factor uniform graphs (II). Indian Journal of Pure and Applied Mathematics, 2022. doi:10.1007/s13226-022-00286-x.
• [29] Zhou S, Wu J, Bian Q. On path-factor critical deleted (or covered) graphs. Aequationes Mathematicae, 2022. 96(4):795-802. doi:10.1007/s00010-021-00852-4.
• [30] Zhou S, Wu J, Liu H. Independence number and connectivity for fractional (a, b, k)-critical covered graphs. RAIRO-Operations Research, 2022. 56(4):2535-2542. doi:10.1051/ro/2022119.
• [31] Zhou S, Wu J, Xu Y. Toughness, isolated toughness and path factors in graphs. Bulletin of the Australian Mathematical Society, 2021. doi:10.1017/S0004972721000952.