Domination Edge Integrity of Corona Products of Pn with Pm,Cm,K1,m

Yıl 2020, , 25 - 31, 24.04.2020

Elgin Kılıç Ayşe Beşirik

https://doi.org/10.33187/jmsm.638124

Cited By: 1

Öz

Vulnerability is the most important concept in analysis of communication networks to disruption. Any network can be modelled by graphs. So measures defined on graphs gives an idea in design. Integrity is one of the well-known vulnerability measures interested in remaining structure of a graph after any failure. Domination is also an another popular concept in network design. Nowadays new vulnerability measures take a great role in network design. Recently designers take into account of any failure not only on nodes also on links which have special properties. A new measure edge domination integrity of a connected and undirected graph was defined by E. Kılıç and A. Beşirik such as ${DI}^{'}(G)=min\{\ |S|+m(G-S):S\ \subseteq \ E(G)\}$ where $m(G-S)$ is the order of a maximum component of $G-S$ and $S$ is an edge dominating set. In this paper some results concerning this parameter on corona products of graph structures $P_n \odot P_m $, $ P_n \odot C_m$, $P_n \odot K_{1,m}$ are presented.

Anahtar Kelimeler

Corona, domination, edge domination, edge integrity

Kaynakça

• [1] F. Buckley, F. Harary, Distance in Graphs, Addison-Wesley Publishing Company, 1990.
• [2] C. A. Barefoot, R. Entringer, H. Swart, Vulnerability in graphs-A comparative survey, J. Combin. Math. Combin. Comput., 1 (1987), 13-22.
• [3] W. Goddard, H. C. Swart, Integrity in graphs: bounds and basics, J.Combin. Math. Combin. Comput, 7 (1990), 139-151.
• [4] K. S. Bagga, L. W. Beineke, W. D. Goddard, M. J. Lipman, R. E. Pippert, Edge-integrity : a survey, Discrete Math., 124 (1994), 3-12.
• [5] T.W.Haynes, S.Hedetniemi, P.Slater, Fundamentals of Domination in Graphs, Marcel Decker Inc., 1998.
• [6] S. Mitchell, S. T. Hedetniemi, Edge domination in trees, Congr. Numer., 19 (1977), 489-509.
• [7] S. Arumugam, S. Velammal, Edge domination in graphs, Taiwanese J. Math., 2(2) (1998), 173-179.
• [8] R. Sundareswaran, V. Swaminathan, Domination integrity in graphs, Proceedings of International Conference on Mathematical and Experimental Physics, (2010), 46-57.
• [9] A. Besirik, E. Kılıc, Domination integrity of some graph classes, RAIRO Oper. Res., 53(5) (2019), 1721-1728.
• [10] E. Kılıc, A. Besirik, Domination edge integrity of graphs, Adv. Math. Models Appl., 3(3) (2018), 234-238.
• [11] A. Besirik, Total domination integrity of graphs, J. Mod. Tech. Eng., 4(1) (2019), 11-19.