BibTex RIS Kaynak Göster

DOMINATION INTEGRITY OF TOTAL GRAPHS

Yıl 2014, Cilt: 4 Sayı: 1, 1 - 10, 01.06.2014

Öz

The domination integrity of a simple connected graph G is a measure of vulnerability of a graph. Here we determine the domination integrity of total graphs of path Pn, cycle Cn and star K1,n.

Kaynakça

  • Bagga, K. S., Beineke, L. W., Goddard, W. D., Lipman, M. J. and Pippert, R. E., (1992), A survey of integrity, Discrete Appl. Math., 37/38 , 13-28.
  • Barefoot, C. A., Entringer, R. and Swart, H., (1987), Vulnerability in Graphs-A Comparative Survey
  • J. Combin. Math. Combin. Comput., 1, 13-22. Behzad, M., (1967), A criterion for the planarity of a total graph, Proc. Cam- bridge Philos. Soc., 63, 681.
  • D¨undar P. and Ayta¸c A.,(2004), Integrity of Total Graphs via Certain Parameters, Mathematical Notes, 76(5), 665-672.
  • Goddard, W. and Swart, H. C., (1990), Integrity in graphs: bounds and basics, J. Combin. Math. Combin. Comput., 7 , 139-151.
  • Harary, F., (1972), Graph Theory, Addison Wesley, Massachusetts.
  • Haynes, T. W., Hedetniemi, S. T. and Slater, P. J., (1998), Fundamentals of Domination in Graphs
  • Monographs and Textbooks in Pure and Applied Mathematics. Marcel Dekker Inc., New York. Mamut, A. and Vumar, E., (2007), A note on the Integrity of Middle Graphs, Lecture Notes in
  • Computer Science, Springer, 4381, 130-134.
  • Sundareswaran, R. and Swaminathan, V., (2010), Domination Integrity in graphs, Proceedings of In- ternational conference on Mathematical and Experimental Physics, Prague, Narosa Publishing House, 57.
  • Sundareswaran, R. and Swaminathan, V., (2010), Domination Integrity of Middle Graphs, In: Alge- bra, Graph Theory and their Applications (edited by T. Tamizh Chelvam, S. Somasundaram and R. Kala), Narosa Publishing House, 88-92.
  • Sundareswaran, R. and Swaminathan, V., (2011), Domination Integrity of Powers of Cycles, Interna- tional Journal of Mathematics Research, 3(3), 257-265.
  • Sundareswaran, R. and Swaminathan, V., (2012), Domination Integrity in trees, Bulletin of Interna- tional Mathematical Virtual Institute, 2, 153-161.
  • Vaidya, S. K. and Kothari, N. J., (2012), Some New Results on Domination Integrity of Graphs, Open
  • Journal of Discrete Mathematics, 2(3), 96-98. doi:10.4236/ojdm.2012.23018
  • Vaidya, S. K. and Kothari, N. J., (2013), Domination Integrity of Splitting Graph of Path and Cycle
  • ISRN Combinatorics, vol. 2013, Article ID 795427, 7 pages. doi:10.1155/2013/795427
  • Vaidya, S. K. and Shah, N. H., Domination Integrity of Shadow Graphs, (2013), In: Advances in
  • Domination Theory II (edited by V. R. Kulli), Vishwa International Publication, India, 19-31.
Yıl 2014, Cilt: 4 Sayı: 1, 1 - 10, 01.06.2014

Öz

Kaynakça

  • Bagga, K. S., Beineke, L. W., Goddard, W. D., Lipman, M. J. and Pippert, R. E., (1992), A survey of integrity, Discrete Appl. Math., 37/38 , 13-28.
  • Barefoot, C. A., Entringer, R. and Swart, H., (1987), Vulnerability in Graphs-A Comparative Survey
  • J. Combin. Math. Combin. Comput., 1, 13-22. Behzad, M., (1967), A criterion for the planarity of a total graph, Proc. Cam- bridge Philos. Soc., 63, 681.
  • D¨undar P. and Ayta¸c A.,(2004), Integrity of Total Graphs via Certain Parameters, Mathematical Notes, 76(5), 665-672.
  • Goddard, W. and Swart, H. C., (1990), Integrity in graphs: bounds and basics, J. Combin. Math. Combin. Comput., 7 , 139-151.
  • Harary, F., (1972), Graph Theory, Addison Wesley, Massachusetts.
  • Haynes, T. W., Hedetniemi, S. T. and Slater, P. J., (1998), Fundamentals of Domination in Graphs
  • Monographs and Textbooks in Pure and Applied Mathematics. Marcel Dekker Inc., New York. Mamut, A. and Vumar, E., (2007), A note on the Integrity of Middle Graphs, Lecture Notes in
  • Computer Science, Springer, 4381, 130-134.
  • Sundareswaran, R. and Swaminathan, V., (2010), Domination Integrity in graphs, Proceedings of In- ternational conference on Mathematical and Experimental Physics, Prague, Narosa Publishing House, 57.
  • Sundareswaran, R. and Swaminathan, V., (2010), Domination Integrity of Middle Graphs, In: Alge- bra, Graph Theory and their Applications (edited by T. Tamizh Chelvam, S. Somasundaram and R. Kala), Narosa Publishing House, 88-92.
  • Sundareswaran, R. and Swaminathan, V., (2011), Domination Integrity of Powers of Cycles, Interna- tional Journal of Mathematics Research, 3(3), 257-265.
  • Sundareswaran, R. and Swaminathan, V., (2012), Domination Integrity in trees, Bulletin of Interna- tional Mathematical Virtual Institute, 2, 153-161.
  • Vaidya, S. K. and Kothari, N. J., (2012), Some New Results on Domination Integrity of Graphs, Open
  • Journal of Discrete Mathematics, 2(3), 96-98. doi:10.4236/ojdm.2012.23018
  • Vaidya, S. K. and Kothari, N. J., (2013), Domination Integrity of Splitting Graph of Path and Cycle
  • ISRN Combinatorics, vol. 2013, Article ID 795427, 7 pages. doi:10.1155/2013/795427
  • Vaidya, S. K. and Shah, N. H., Domination Integrity of Shadow Graphs, (2013), In: Advances in
  • Domination Theory II (edited by V. R. Kulli), Vishwa International Publication, India, 19-31.
Toplam 19 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Research Article
Yazarlar

S. K. Vaidya Bu kişi benim

N. H. Shah Bu kişi benim

Yayımlanma Tarihi 1 Haziran 2014
Yayımlandığı Sayı Yıl 2014 Cilt: 4 Sayı: 1

Kaynak Göster