Detour Global Domination for Degree Splitting graphs of some graphs

C. Jayasekaran, S.V. Ashwin Prakash

Abstract


In this paper, we introduced the new concept detour global domination number for degree splitting graph of standard graphs. The detour global dominating sets in some standard and special graphs are determined. First we recollect the concept of degree splitting graph of a graph and we produce some results based on the detour global domination number of degree splitting graph of star graph, bistar graph, complete bipartite graph, complete graph path graph, cycle graph, wheel graph and helm graph. A set S is called a detour global dominating set of G if S is both detour and global dominating set of G. The detour global domination number is the minimum cardinality of a detour global dominating set in G.

Keywords


Detour set, Dominating set, Detour Domination, Global Domination, Detour Global Domination, Degree Splitting graphs

Full Text:

PDF

References


F.Buckley and F.Harary, Distance in Graphs, Addison-Wesley,Redwood City, (1990).

G. Chartrand, N. Johns and P. Zang, Detour Number of a graph, Util. Math. 64 97-113 (2003).

T.W. Haynes, S.T. Hedetniemi and P.J. Slater Fundamentals of Domination in Graphs,Marcel Dekker,Inc., New York, (1998).

C. Jayasekaran, S.V. Ashwin Prakash, Detour global domination number of some graphs, Malaya Journal of Matematik, S(1), 552-555, (2020).

E. Sampath Kumar, The Global Domination Number of a Graph, Journal of Mathematical and Physical Sciences, 23(5),377-385 (1989).

R. Ponraj, S. Somasundaram On the degree splitting graph of a graph, National Academy Science Letters, 27(7-8), 275-278, (2004).

D.B. West, Introduction to Graph Theory,Second Ed., Prentice-Hall, Upper Saddle River, NJ,(2001




DOI: http://dx.doi.org/10.23755/rm.v47i0.871

Refbacks

  • There are currently no refbacks.


Copyright (c) 2023 C. Jayasekaran, S.V. Ashwin Prakash

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.

Ratio Mathematica - Journal of Mathematics, Statistics, and Applications. ISSN 1592-7415; e-ISSN 2282-8214.