Bazı Tümleyen Prizma Grafların Arasındalık Merkezliği
Year 2019,
, 277 - 283, 25.08.2019
Aysun Aytaç
,
Canan Çiftçi
Abstract
Literatürde ağlar için tanımlanmış birçok merkezlik ölçümü vardır. Bunlardan biri arasındalık merkezliğidir. Arasındalık merkezliği bir tepenin tüm tepe çiftleri arasındaki bilgi akışına etkisinin bir ölçümüdür. Bu bilgi akışı, tepeler arasındaki en kısa yollar üzerinde olmaktadır. Herhangi bir tepenin yüksek arasındalık merkezliğe sahip olması o tepenin birbiriyle komşu olmayan tepelerle ne düzeyde bağlantı içinde olduğunu göstermektedir. Bu tepe ağdaki bilgi akışını kontrol ettiğinden ağda önemli bir yere sahiptir. Bu makalede bazı tümleyen prizma grafların arasındalık merkezliği üzerine çalışılmıştır.
References
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Betweenness Centrality of Some Complementary Prism Graphs
Year 2019,
, 277 - 283, 25.08.2019
Aysun Aytaç
,
Canan Çiftçi
Abstract
There are a lot of centrality measures that have been introduced for networks. One of them is betweenness centrality. It is a measure of the influence of a vertex over the flow of information between all pairs of vertices. This information flows over the shortest paths between these vertices. The fact that any vertex has a high value of centrality indicates that what level this vertex is in connection with vertices which are not adjacent with each other. Since this vertex controls flows of information, it has a potential role in the network. In this paper, we study on the betweenness centrality of some complementary prism graphs.
References
- [1] Bader, D. A., Kintali, S., Madduri, K., Mihail, M. 2007. Approximating Betweenness Centrality. In International Workshop on Algorithms and Models forthe Web-Graph, 124-137. Springer Berlin Heidelberg.
- [2] Raghavan Unnithan, S. K., Kannan, B., Jathavedan, M. 2014. Betweenness Centrality in Some Classes of Graphs. International Journal of Combinatorics, 2014, Article ID 241723, 12 pages.
- [3] Otte, E., Rousseau, R. 2002. Social Network Analysis: a powerful strategy, also for the information sciences. Journal of information Science, 28(6), 441-453.
- [4] Latora, V., Marchiori, M. 2007. A Measure of Centrality Based on Network Efficiency. New Journal of Physics, 9(6), 188.
- [5] Estrada, E. 2006. Virtual Identification of Essential Proteins within the Protein Interaction Network of Yeast. Proteomics, 6(1), 35-40.
- [6] Rubinov, M., Sporns, O. 2010. Complex Network Measures of Brain Connectivity: uses and interpretations. Neuroimage, 52(3), 1059-1069.
- [7] Dehmer, M., Emmert-Streib, F. (Eds.). 2014. Quantitative Graph Theory: Mathematical Foundations and Applications. CRC press, 516p.
- [8] Bavelas, A. 1948. A Mathematical Model for Group Structures. Human organization. 7(3), 16-30.
- [9] Freeman, L. C. 1977. A Set of Measures of Centrality Based on Betweenness. Sociometry, 40(1), 35-41.
- [10] Haynes, T. W., Henning, M. A., Slater, P. J., van der Merwe, L. C. 2007. The Complementary Product of Two Graphs. Bulletin of the Institute of Combinatorics and its Applications, 51, 21-30.
- [11] Cappelle, M. R., Coelho, E. M., Coelho, H., Penso, L. D., Rautenbach, D. 2015. Identifying Codes in the Complementary Prism of Cycles. arXiv preprintarXiv:1507.05083.
- [12] Haynes, T. W., Henning, M. A., van der Merwe, L. C. 2009. Domination and Total Domination in Complementary Prisms. Journal of Combinatorial Optimization, 18(1), 23-37.
- [13] Chaluvaraju, B., Chaitra, V. 2012. Roman domination in complementary prism graphs. Mathematical Combinatorics, 2, 24-31.
- [14] Desormeaux, W. J., Haynes, T.W., Vaughan, L. 2013. Double domination in complementary prisms. Utilitas Mathematica, 91, 131-142.
- [15] Kazemi, A. P. 2012. k-Tuple Total Domination in Complementary Prisms. ISRN Discrete Mathematics, 2011.
- [16] Chartrand, G., Lesniak, L., Zhang, P. 2010. Graphs & Digraphs, Fifth Edition. Taylor & Francis. CRC Press. 586p.