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The concept of vulnerability is very important in network analysis. Several existing parameters have been proposed in the literature to measure network vulnerability, such as domination number, average lower domination number, residual domination number, average lower residual domination number, residual closeness and link residual closeness. In this paper, incorporating the concept of the domination number and link residual closeness number, as well as the idea of the average lower domination number, we introduce new graph vulnerability parameters called the link residual domination number, denoted by γLR(G), and the average lower link residual domination number, denoted by γLRaν(G) , for any given graph G. Furthermore, the exact values and the upper and lower bounds for any graph G are given, and the exact results of well-known graph families are computed.
Wydawca
Czasopismo
Rocznik
Tom
Strony
43--59
Opis fizyczny
Bibliogr. 35 poz., rys., tab.
Twórcy
autor
- Department of Mathematics, Faculty of Science, Karabuk University, 78050 Karabuk, Turkey
Bibliografia
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- [11] Aslan E. Edge-rupture degree of a graph. Dyn. Contin. Discrete Impuls. Syst. Ser. B Appl. Algorithms, 2015. 22(2):4.
- [12] Li Y, Zhang S, Li X. Rupture degree of graphs. International Journal of Computer Mathematics, 2005. 82(7):793-803. doi:10.1080/00207160412331336062.
- [13] Henning MA, Oellermann OR. The average connectivity of a digraph. Discrete Applied Mathematics, 2004. 140(1-3):143-153. doi:10.1016/j.dam.2003.04.003.
- [14] Beineke LW, Oellermann OR, Pippert RE. The average connectivity of a graph. Discrete mathematics, 2002. 252(1-3):31-45. doi:10.1016/S0012-365X(01)00180-7.
- [15] Blidia M, Chellali M, Maffray F. On average lower independence and domination numbers in graphs. Discrete mathematics, 2005. 295(1-3):1-11. doi:10.1016/j.disc.2004.12.006.
- [16] Henning MA. Trees with equal average domination and independent domination numbers. Ars Combinatoria, 2004. 71:305-318.
- [17] Tuncel Golpek H, Turaci T, Coskun B. The Average Lower Domination Number and Some Results of Complementary Prisms and Graph Join. J. Adv. Res. Appl. Math, 2015. 7(1):52-61. doi:10.5373/jaram.2056.053014.
- [18] Aslan E. The average lower connectivity of graphs. Journal of Applied Mathematics, 2014. 2014. doi:10.1155/2014/807834.
- [19] Turaci T. On the average lower bondage number of a graph. RAIRO-Operations Research, 2016. 50(4-5):1003-1012. doi:10.1051/ro/2015062.
- [20] Turaci T, Aslan E. The average lower reinforcement number of a graph. RAIRO-Theoretical Informatics and Applications, 2016. 50(2):135-144. doi:10.1051/ita/2016015.
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- [25] Dangalchev C. Residual closeness in networks. Physica A: Statistical Mechanics and its Applications, 2006. 365(2):556-564. doi:10.1016/j.physa.2005.12.020.
- [26] Dangalchev C. Residual Closeness of Generalized Thorn Graphs. Fundamenta Informaticae, 2018. 162(1):1-15. doi:10.3233/FI-2018-1710.
- [27] Dangalchev C. Residual closeness and generalized closeness. International Journal of Foundations of Computer Science, 2011. 22(08):1939-1948. URL https://doi.org/10.1142/S0129054111009136.
- [28] Aytac A, Odabas ZN. Residual closeness of wheels and related networks. International Journal of Foundations of Computer Science, 2011. 22(05):1229-1240. doi:10.1142/S0129054111008660.
- [29] Aytaç A, Berberler ZNO. Robustness of regular caterpillars. International Journal of Foundations of Computer Science, 2017. 28(07):835-841. URL https://doi.org/10.1142/S0129054117500277.
- [30] Turaci T, Okten M. Vulnerability of mycielski graphs via residual closeness. Ars Combinatoria, 2015. 118:419-427.
- [31] Berberler ZN, Yigit E. Link vulnerability in networks. International Journal of Foundations of Computer Science, 2018. 29(03):447-456. URL https://doi.org/10.1142/S0129054118500144.
- [32] Odabaş ZN, Aytaç A. Residual closeness in cycles and related networks. Fundamenta Informaticae, 2013. 124(3):297-307. doi:10.3233/FI-2013-835.
- [33] Yiğit E, Berberler ZN. A Note on the Link Residual Closeness of Graphs Under Join Operation. International Journal of Foundations of Computer Science, 2019. 30(03):417-424. URL https://doi.org/10.1142/S0129054119500126.
- [34] Rupnik Poklukar D, Žerovnik J. Networks with Extremal Closeness. Fundamenta Informaticae, 2019. 167(3):219-234. doi:10.3233/FI-2019-1815.
- [35] Turacı T, Aytaç A. Combining the Concepts of Residual and Domination in Graphs. Fundamenta Informaticae, 2019. 166(4):379-392. doi:10.3233/FI-2019-1806.
Uwagi
Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2020).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-f7fbbcef-0752-4bf1-93fb-af0fd0be0f60