Abstract:
Communication networks have been characterized by high levels of service reliability. Links cuts, node interruptions, software errors or hardware failures, and transmission failures at various points can interrupt service for long periods of time. In communication networks, greater degrees of stability or less vulnerability is required. The vulnerability of communication network measures the resistance of the network to the disruption of operation after the failure of certain stations or communication links. If we think of a graph G as modeling a network, many graph-theoretic parameters can be used to describe the stability of communication networks, including connectivity, integrity, and tenacity. We consider two graphs with the same connectivity, but with unequal orders of theirs largest components. Then these two graphs must be different in respect to stability. How can we measure that property? The idea behind the answer is the concept of integrity, which is different from connectivity. Total graphs constitute a large class of graphs. In this paper, we study the integrity of total graphs via some graph parameters.
Citation:
P. Dündar, A. Aytaç, “Integrity of Total Graphs via Certain Parameters”, Mat. Zametki, 76:5 (2004), 714–722; Math. Notes, 76:5 (2004), 665–672
This publication is cited in the following 17 articles:
Cauê F. Teixeira da Silva, Daniel Posner, Renato Portugal, “Walking on vertices and edges by continuous-time quantum walk”, Quantum Inf Process, 22:2 (2023)
Basavanagoud B., Jakkannavar P., Policepatil Sh., “Integrity of Total Transformation Graphs”, Electron. J. Graph Theory Appl., 9:2 (2021), 309–329
Basavanagoud B., Policepatil Sh., “Integrity of Wheel Related Graphs”, Punjab Univ. J. Math., 53:5 (2021), 329–338
Besirik A., Kilic E., “Domination Integrity of Some Graph Classes”, Rairo-Oper. Res., 53:5 (2019), 1721–1728
Dundar P. Aytac A. Kilic E., “Common-Neighbourhood of a Graph”, Bol. Soc. Parana. Mat., 35:1 (2017), 23–32
Kilic E., Dundar P., “Total Accessibility Number of Graphs”, Neural Netw. World, 27:3 (2017), 309–315
Mahde S.S., Mathad V., “Domination Integrity of Line Splitting Graph and Central Graph of Path, Cycle and Star Graphs”, Appl. Appl. Math., 11:1 (2016), 408–423
Vaidya S.K., Kothari N.J., “Domination Integrity of Splitting and Degree Splitting Graphs of Some Graphs”, Adv. Appl. Discret. Math., 17:2 (2016), 185–199
Mahde S.S., Mathad V., “Hub-Integrity of Splitting Graph and Duplication of Graph Elements”, TWMS J. Appl. Eng. Math., 6:2 (2016), 289–297
V. V. Bykova, “O merakh tselostnosti grafov: obzor”, PDM, 2014, no. 4(26), 96–111
Samir K. Vaidya, Nirang J. Kothari, “Domination Integrity of Splitting Graph of Path and Cycle”, ISRN Combinatorics, 2013 (2013), 1
Samir K. Vaidya, Nirang J. Kothari, “Some New Results on Domination Integrity of Graphs”, OJDM, 02:03 (2012), 96
Kilic E., Dundar P., “The edge-accessibility number via graph, operations & an algorithm”, Neural Network World, 17:3 (2007), 213–223
Mamut A., Vumar E., “A Note on the Integrity of Middle Graphs”, Discrete Geometry, Combinatorics and Graph Theory, Lecture Notes in Computer Science, 4381, eds. Akiyama J., Chen W., Kano M., Li X., Yu Q., Springer-Verlag Berlin, 2007, 130–134
Dundar P., Kilic E., “Two measures for the stability of Extended Fibonacci Cubes”, Neural Network World, 16:5 (2006), 411–419
Dündar P., “Augmented cubes and its connectivity numbers”, Neural Network World, 15:1 (2005), 1–8
Citation in format AMSBIB
Contact us: