Total Domination Number in Graphs and Graph Modification

  IJMTT-book-cover
 
International Journal of Mathematics Trends and Technology (IJMTT)
 
© 2020 by IJMTT Journal
Volume-66 Issue-9
Year of Publication : 2020
Authors : V.Anithakumari, M.Padmini
  10.14445/22315373/IJMTT-V66I9P512

MLA

MLA Style: V.Anithakumari, M.Padmini "Total Domination Number in Graphs and Graph Modification" International Journal of Mathematics Trends and Technology 66.9 (2020):99-104. 

APA Style: V.Anithakumari, M.Padmini(2020). Total Domination Number in Graphs and Graph Modification International Journal of Mathematics Trends and Technology, 99-104.

Abstract
The major purpose of this paper is to study the effect that various graph modifications have on the total domination number of a graph. In addition, we study the effect that the operation of edge lifting has on the domination number of a graph. We finish this work with a study of the total domination number of diameter two graphs and the relationship between the total domination number of a graph and its total destruction number.

Reference

[1] Abdulgani sahin e.al (2020), Total Edge- Vertex Domination, Theatrical Information and Application, Vol:4, Issue:2,pp:123-129.
[2] Al-Harere et.al (2019), Change of Tadpole domination number upon changing of Graph, Journal of Science And Integellince, Vol:31, Issue 2,pp:197-199.
[3] Bauer .D et al (2012), Domination alteration sets in graphs, Discrete Applied Mathematics, Vol:1, Issue:2 ,pp:1143-1151.
[4] Bohdan Zelinka et al (2019), Signed Total Domination Number of a Graph, Journal of Mathematics , Vol 51,Issue:26,pp:225-229.
[5] Haynes T.W et al(2012), External 2-2 insensitive graphs, Discrete Applied Mathematics, Vol:10,Issue:7,pp:1143-1151
[6] Haynes T.W et.al (2018), External graphs domination insensitive to the removal of k-edges, Applied Mathematics, Vol:5, Issue:2 ,pp:114-119.
[7] Kulli V.R(2015), The Total dominating Graph ,Annals of Pure and Applied Mathematics , Vol:10,Issue:1,pp:123-128.
[8] Latheesh Kumar e al (2016), A Note on Global Bipartite Domination in Graph, Malaya Journal Matemaik, Vol:4, Issue:3, pp:438-442.
[9] Meenal et al (2019), Average Total Domination Number on Graph, International Journal of Emerging Technologies and Innovative Research, Vol:1, Issue 1,pp:54-66.
[10] Manjusha et al (2015), Strong domination in Fuzzy Graph, Academic Research paper on Mathematics ,Vol:7, pp:369-377.
[11] Nader Jefari Rad et al (2012), On Alpha total domination in graph, Discrete Applied Mathematics, Vol:10,Issue:7,pp:1143-1151.
[12] Ramy Shaheen et.al (2017),On the 2-Domination Number of Complete Grid Graph, Open Journal of Discrete Mathematics, Vol:7,No:1,
[13] Radha Rajamani Iyar (2014), The co-total domination number of a graph, Journal of Discreate Mathemaical Science and cryptography, Vol:2, Issue:2, pp123-128.

Keywords : Dominating Graph, Stable Graphs, Edge Critical Graphs, Domination Number.