Abstract
References
- A. Brandstädt, V. B. Le, J. P. Spinrad: Graph classes: a survey, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 1999.
- A. Aytaç, and Z. N. Odabaş: Residual Closeness of Wheels and Related Networks, Internat. J. Found. Comput. Sci., 22 , 1229-1240, 2011.
- C. A. Barefoot, R. Entringer and H. Swart: Vulnerability in graphs–a comparative survey, J. Combin. Math. Combin. Comput., 1, 13 - 22, 1987.
- D. R. Woodall: The binding number of a graph and its Anderson number, Journal of Combinatorial Theory, Series B, 15, 225 - 255, 1973.
- F. Buckley and F. Harary: Distance in Graphs, Addison-Wesley Publishing Company Advanced Book Program, Redwood City, CA, 1990.
- F. Comellas, S. Gago: Spectral bounds for the betweenness of a graph, Linear Algebra Appl., 423, 74 - 80, 2007.
- G. Chartrand and L. Lesniak: Graphs and Digraphs, Second Edition, Wadsworth & Brooks/Cole Advanced Books & Software, Monterey, CA, 1986.
- H. A. Jung: On a class of posets and the corresponding comparability graphs, Journal of Combinatorial Theory, Series B, 24 (2), 125 - 133, 1978.
- H. Frank, I. T. Frisch: Analysis and design of survivable networks, IEEE Transactions on Communications Technology, 18(5), 501 - 519, 1970.
- I. Javaid, S. Shokat: On the partition dimension of some wheel related graphs, Journal of Prime Research in Mathematics, 4, 154 - 164, 2008.
- J. A. Gallian: A dynamic survey of graph labeling, Elect. Jour. Combin., 15, DS6, 2008.
- M. Arockiaraj, P. Manuel, I. Rajasingh, B. Rajan: Wirelength of 1-fault hamiltonian graphs into wheels and fans Inform. Process. Lett., 111, 921-925, 2011.
- L. C. Freeman: A set of measures of centrality based on betweenness, Sociometry, 40, No. 1, 35 - 41, 1977.
- S. Gago, J. Hurajová and T. Madaras: Notes on the betweenness centrality of a graph, Math. Slovaca, 62, No. 1, 1-12, 2012.
- T. Turaci and M. Ökten : Vulnerability Of Mycielski Graphs Via Residual Closeness, Ars Combinatoria, Volume CXVIII, 419 - 427, 2015.
- V. Aytac and T. Turaci: Computing the closeness Centrality in Some Graphs, Submitted.
- Z. N. Odabaş and A. Aytaç: Residual Closeness in Cycles and Related Networks, Fundamenta Informaticae, 124, 297 - 307, 2013.
Abstract
A central issue in the analysis of complex networks is
the assessment of their stability and vulnerability. A variety of measures have
been proposed in the literature to quantify the stability of networks and a
number of graph-theoretic parameters have been used to derive formulas for
calculating network reliability. Different measures for graph vulnerability
have been introduced so far to study different aspects of the graph behavior
after removal of vertices or links such as connectivity, toughness, scattering
number, binding number, residual closeness and integrity. In this paper, we
consider betweenness centrality of a graph. Betweenness centrality of a vertex
of a graph is portion of the shortest paths all pairs of vertices passing
through a given vertex. In this paper, we obtain exact values for betweenness
centrality for some wheel related graphs namely gear, helm, sunflower and
friendship graphs.
Keywords
Network vulnerability Network design and communication Stability Betweenness centrality of a graph Gear graph Helm graph
References
- A. Brandstädt, V. B. Le, J. P. Spinrad: Graph classes: a survey, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 1999.
- A. Aytaç, and Z. N. Odabaş: Residual Closeness of Wheels and Related Networks, Internat. J. Found. Comput. Sci., 22 , 1229-1240, 2011.
- C. A. Barefoot, R. Entringer and H. Swart: Vulnerability in graphs–a comparative survey, J. Combin. Math. Combin. Comput., 1, 13 - 22, 1987.
- D. R. Woodall: The binding number of a graph and its Anderson number, Journal of Combinatorial Theory, Series B, 15, 225 - 255, 1973.
- F. Buckley and F. Harary: Distance in Graphs, Addison-Wesley Publishing Company Advanced Book Program, Redwood City, CA, 1990.
- F. Comellas, S. Gago: Spectral bounds for the betweenness of a graph, Linear Algebra Appl., 423, 74 - 80, 2007.
- G. Chartrand and L. Lesniak: Graphs and Digraphs, Second Edition, Wadsworth & Brooks/Cole Advanced Books & Software, Monterey, CA, 1986.
- H. A. Jung: On a class of posets and the corresponding comparability graphs, Journal of Combinatorial Theory, Series B, 24 (2), 125 - 133, 1978.
- H. Frank, I. T. Frisch: Analysis and design of survivable networks, IEEE Transactions on Communications Technology, 18(5), 501 - 519, 1970.
- I. Javaid, S. Shokat: On the partition dimension of some wheel related graphs, Journal of Prime Research in Mathematics, 4, 154 - 164, 2008.
- J. A. Gallian: A dynamic survey of graph labeling, Elect. Jour. Combin., 15, DS6, 2008.
- M. Arockiaraj, P. Manuel, I. Rajasingh, B. Rajan: Wirelength of 1-fault hamiltonian graphs into wheels and fans Inform. Process. Lett., 111, 921-925, 2011.
- L. C. Freeman: A set of measures of centrality based on betweenness, Sociometry, 40, No. 1, 35 - 41, 1977.
- S. Gago, J. Hurajová and T. Madaras: Notes on the betweenness centrality of a graph, Math. Slovaca, 62, No. 1, 1-12, 2012.
- T. Turaci and M. Ökten : Vulnerability Of Mycielski Graphs Via Residual Closeness, Ars Combinatoria, Volume CXVIII, 419 - 427, 2015.
- V. Aytac and T. Turaci: Computing the closeness Centrality in Some Graphs, Submitted.
- Z. N. Odabaş and A. Aytaç: Residual Closeness in Cycles and Related Networks, Fundamenta Informaticae, 124, 297 - 307, 2013.
Details
| Primary Language | English |
|---|---|
| Journal Section | Articles |
| Authors | |
| Publication Date | October 1, 2017 |
| Published in Issue | Year 2017 Volume: 5 Issue: 4 |
