IJSTR

International Journal of Scientific & Technology Research

Home Contact Us
ARCHIVES
ISSN 2277-8616











 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

IJSTR >> Volume 8 - Issue 9, September 2019 Edition



International Journal of Scientific & Technology Research  
International Journal of Scientific & Technology Research

Website: http://www.ijstr.org

ISSN 2277-8616



Detour Domination In Soft Graph

[Full Text]

 

AUTHOR(S)

N. Sarala, K. Manju

 

KEYWORDS

detour distance, total detour set, detour dominating set, minimal detour dominating set, upper detour dominating number in soft graphs.

 

ABSTRACT

A set D of vertices of a soft graph (F, A) is said to be a dominating set if every vertex of the subgraph induced by F(x) in V −D is adjacent to a vertex in D. In this paper, the concepts of detour domination in soft graph and some types of detour domination in soft graphs including detour distance, total detour distance, detour dominating set, minimal detour dominating set, upper detour dominating number in soft graphs are introduced and investigating some of their properties and results.

 

REFERENCES

[1]. M.Akram and S.Nawaz, Operation on soft graphs, Fuzzy Information and Engineering, 7(4) (2015) 423-449.
[2]. F. Buckley and F. Harary, Distance in Graphs, AddisonWesley, Redwood City, 1990.
[3]. G. Chartrand, T. W. Haynes, M. A. Henning and P. Zhang, Detour domination in graphs, Ars Combinatoria, 71(2004), 149-160.
[4]. G.Chartrand, G. L.JohnsandS.Tian, Detour distance in graph, Annals of Discrete Mathematics, 55(1993), 127-136.
[5]. G. Chartrand, G. L. Johns and P. Zhang, The detour number of a graph, Util. Math., 64(2003), 97-113.
[6]. G. Chartrand, G. L. Johns and P. Zhang, On the detour number and geodetic number of a graph, Ars combinatoria, 72(2004), 3-15.
[7]. G. Chartrand and P. Zhang, Distance in graphs - Taking the long view, AKCE J. Graphs. Combin., 1(1)(2004), 1-13.
[8]. T.W. Haynes, S.T. Hedetniemi and P.J. Slater,Fundamentals of domination in Graphs, Marcel Dekker, NewYork, (1998).
[9]. J. John and N. Arianayagam, The detour domination number of a graph, Discrete Mathematics, Algorithms and Applications, 9(1)(2017), 1750006 (7 pages).
[10]. J. John and N. Arianayagam, The Upper Detour Domination Number of a Graph, International Journal of Engineering Science, Advanced Computing and Bio-Technology , Jan 201724 – 29.
[11]. D.A.Molodtsov, Soft set theory-first results, Computers and Mathematics with Application, 37 (199) 19-31.
[12]. Rajesh K. Thumbakara and Bobin George, Soft Graphs, ICSRS Publication, Vol. 2, April 2014, pp. 75-86
[13]. Samir K.Vaidya and Raksha N.Mehta, international journal of mathematics and scientific computing, 2(2015),89-91.
[14]. Sarala.N, Manju.K, Some types of domination in Soft Graph ,International Journal of Research and Analytical Reviews , June 2019, Volume 6, Issue 2,968-973.
[15]. S.K.Vaidya and S.H.Karkar, Detour domination number of some cycle related graphs, (communicated).
[16]. S. K. Vaidya and R. N. Mehta, On detour domination in graphs, International Journal of Mathematics and Scientific Computing, 11(2016), 397-407.
[17]. S. K. Vaidya and S. H. Karkar, Detour domination number of some path and cycle related graphs, Malaya Journal of Matematik, Vol. 7, No. 1, 2019,15-19.