Volume 55 | Number 2 | Year 2018 | Article Id. IJMTT-V55P519 | DOI : https://doi.org/10.14445/22315373/IJMTT-V55P519

The study of independence and domination numbers of graphs is that the quickest growing space in graph theory. Domination number and independence numbers area unit utilized in such fields as algorithmic styles, social sciences, communication networks etc. A set D of vertices is the dominating set of graph G if each vertex of V to D is adjacent to different vertex of D. The domination number of graph is that the minimum cardinality of a dominating set of G, it's denoted by gamma(G). Independence number is that the highest cardinality of associate degree independent set of vertices of a graph Domination range is that the cardinality of a minimum dominating set of a graph. During this paper we tend to are presenting results on domination and independence numbers of tetra bipartite graphs.

[1] Narsingh Deo, “Graph Theory with Applications to Engineering and Comp.Science”, Prentice Hall, Inc., USA ,1974.

[2] C. Payan and N. H. Xuong, “Domination-balanced graphs”, J. Graph Theory 6, 1982, 23-32.

[3] E. J. Cockayne and S. T. Hedetniemi, “Towards a theory of domination in graphs”, Networks, 7, 1977, 247 -261. MAYFEB Journal of Mathematics - ISSN 2371-6193 Vol 3 (2017) - Pages 20-27 26

[4] F. S. Roberts, “Graph theory and its application to problems of society”, SIAM, Philadelphia, 1978, 57-64.

[5] J.F. Fink, M.S. Jacobson, L. Kinch and J. Roberts, “On graphs having domination number half their order”, Period. Math. Hungar, 16, 1985, 287–293.

[6] M. Blidia, M. Chellali and O. Favaron, “Independence and 2-domination in trees”, Australas. J. Combin. 33, 2005, 317–327.

[7] N. Murugesan and Deepa S. Nair “The Domination and Independence of Some cubic Bipartite Graphs” Int. J. Contemp. Math. Sciences, Vol.6, no. 13, 2011, pp. 611 – 618.

[8] B. Zelinka, “Some remarks on domination in tetragraphs”, Discrete Mathematics, 158, 1996, 249-255.

[9] O. Ore, “Theory of Graphs”, Amer. Math. Soc. Colloq. Publ. 38, (1962).

[10] T.W Haynes, S.T. Hedetniemi S. T. and P. J. Slater. “Fundamentals of domination in Graphs”, Marcel Dekker, New York, 1998.

[11] T. W. Haynes, S. T. Hedetniemi, P. J. Slater, “Domination in graphs, Advanced Topics”, Marcel Dekker, New York, 1998.

[12] Vasumathi, N., and Vangipuram, S., Existence of a graph with a given domination parameter, Proceedings of the Fourth Ramanujan Symposium on Algebra and its Applications, University of Madras, Madras, 187-195 (1995).

[13] Vijaya Saradhi and Vangipuram, Irregular graphs‟. Graph Theory Notes of New York, Vol. 41, 33-36, (2001).

Varta Teotia, Sapna Shrimali, "Sum of Domination and Independence Numbers of Tetra Bipartite Graphs," *International Journal of Mathematics Trends and Technology (IJMTT)*, vol. 55, no. 2, pp. 153-157, 2018. *Crossref*, https://doi.org/10.14445/22315373/IJMTT-V55P519