DOMINATION INTEGRITY OF TOTAL GRAPHS

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

S. K. Vaidya N. H. Shah

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.

Keywords

Integrity , Domination Integrity , total graph

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.