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DOMINATION INTEGRITY OF TOTAL GRAPHS

Year 2014, Volume: 4 Issue: 1, 1 - 10, 01.06.2014

Abstract

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.

References

  • 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.
Year 2014, Volume: 4 Issue: 1, 1 - 10, 01.06.2014

Abstract

References

  • 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.
There are 19 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

S. K. Vaidya This is me

N. H. Shah This is me

Publication Date June 1, 2014
Published in Issue Year 2014 Volume: 4 Issue: 1

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