Connectivity of the planar graph with highly reliable edges
Prikladnaâ diskretnaâ matematika, no. 3 (2012), pp. 103-107.

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In this paper, an algorithm based on the concept of dual graphs is constructed for calculation of incoherence probability for planar graphs with the high reliable edges. Numerical experiments show that, in a comparison with the Monte-Carlo method, this algorithm decreases calculation complexity significantly.
Keywords: connectivity probability, dual graph, minimal cross section.
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G. Sh. Tsitsiashvili; A. S. Losev. Connectivity of the planar graph with highly reliable edges. Prikladnaâ diskretnaâ matematika, no. 3 (2012), pp. 103-107. http://geodesic.mathdoc.fr/item/PDM_2012_3_a11/

[1] Tsitsiashvili G. Sh., “Complete calculation of disconnection probability in planar graphs”, Reliability: Theory and Applications, 1(24):1 (2012), 154–159

[2] Burtin Yu., Pittel B., “Asimptoticheskie otsenki nadëzhnosti slozhnykh sistem”, Tekhnicheskaya kibernetika, 10:3 (1972), 90–96 | MR

[3] Whithney H., “Nonseparable and planar graphs”, Trans. American Math. Soc., 34 (1932), 39–362

[4] Harary F., Manvel B., “On the Number of Cycles in a Graph”, Matematickycasopis, 21:1 (1971), 55–63 | MR | Zbl

[5] Prasolov V. V., Elementy kombinatornoi i differentsialnoi topologii, MTsNMO, M., 2004, 352 pp.

[6] Zolotukhin I. V., “Uglerodnye nanotrubki”, Sorosovskii obrazovatelnyi zhurnal, 1999, no. 3, 111–115