Blended Dominance Property Embedded in Graphs

  IJMTT-book-cover
 
International Journal of Mathematics Trends and Technology (IJMTT)
 
© 2018 by IJMTT Journal
Volume-62 Number-1
Year of Publication : 2018
Authors : Sreejil K, Rajakumari N
  10.14445/22315373/IJMTT-V62P503

MLA

MLA Style: Sreejil K, Rajakumari N "Blended Dominance Property Embedded in Graphs" International Journal of Mathematics Trends and Technology 62.1 (2018): 14-15.

APA Style: Sreejil K, Rajakumari N (2018). Blended Dominance Property Embedded in Graphs. International Journal of Mathematics Trends and Technology, 62(1), 14-15.

Abstract
Domination in graphs has been the core competency study topic at the outbreak of this era. Its profound and exclusive study of domination is graphs kick started around1850, coupled with the challenges of placing the least number of queens on an n x n chess board. So as to cover, there by dominating every square. Neverthless the challenges till date remains unanswered and clueless, the domination of graphs and its rise, dwells at length on graph theory introduced by Ore and Berge, they delves deep into researches most significant schools of thought and innovations. Berge presents the challenges of five queens namely place five queens on the chess board, so that unsparingly every square is covered by at least one queen. The solutions to these problems are dominating sets in graph, whose vertices are the queens of the chess board and vertices u, v are adjacent if a queen move from u to v is single move. This paves the way to domination in graphs. Starting with a close examination of one’s own concept of domination in graphs ranges far and wide to give specific answers to all the challenges poping up.

References
[1] E.J. Cockayne, R.M. Dawes, and S. T .Hedetniemi, Total domination in graphs, Networks 10 (1980), 211–219.
[2] Kumar S.S., Rao M.R.K., Balasubramanian M.P., "Anticarcinogenic effects of indigofera gaspalathoides on 20-methylcholanthrene induced fibrosarcoma in rats", Research Journal of Medicinal Plant, ISSN : 5(6) (2011) PP. 747-755.
[3] M. Borowiecki and D.Michalak, Generalized Independence and domination in graphs, Discrete Mathematics 191 (1998), 51–56.
[4] Beula Devamalar P.M., Thulasi Bai V., Srivatsa S.K., "Design and architecture of real time web-centric tele health diabetes diagnosis expert system", International Journal of Medical Engineering and Informatics, ISSN : 1755-0661, 1(3) (2009) PP.307-317.
[5] T. W. Haynes, S. T. Hedetniemi, and P. J. Slater, Fundamentals of Domination in Graphs, Marcel Dekker, Inc., New York, 1998.
[6] Niranjan U., Subramanyam R.B.V., Khanaa V., "Developing a Web Recommendation System Based on Closed Sequential Patterns",fCommunications in Computer and Information Science, ISSN : 1865-0929, 101() (2010) PP.171-179.
[7] J. Harant and M. A. Henning, On double domination in graphs, Discussiones Mathematicae Graph Theory 25 (2005), 29–34.
[8] T. W. Haynes, S. T. Hedetniemi, and P. J. Slater, eds. Domination in Graphs: Advanced Topics, Marcel Dekker, Inc., New York, 1998.
[9] Jaikumar S., Ramaswamy S., Asokan B.R., Mohan T., Gnanavel M., "Anti ulcer activity of methanolic extract of Jatropha curcas (Linn.) on Aspirin-induced gastric lesions in wistar strain rats", Research Journal of Pharmaceutical, Biological and Chemical Sciences, ISSN : 0975- 8585, 1(4) (2010) PP.886-897.
[10] W Sharmila S., Jeyanthi Rebecca L., Saduzzaman M., "Biodegradation of domestic effluent using different solvent extracts of Murraya koenigii", Journal of Chemical and Pharmaceutical Research, ISSN : 0975 – 7384, 5(2) (2013) PP.279-282.
[11] Goddard and M. A. Henning, Generalised domination and independence in graphs, Congressus Numerantium 123 (1997), 161–171.

Keywords
Graph theory, domination in graph.