The nonsplit domination in subdivision graphs
Keywords:Domination number, Nonsplit domination number, Subdivision graph, Nonsplit domination number of subdivision graph
A dominating set D of a graph G = (V, E) is a nonsplit dominating set if the induced subgraph 〈V − D〉 is connected. The nonsplit domination number γns(G) of G is the minimum cardinality of a nonsplit dominating set. An edge e = uv of a graph G is said to be subdivided if e is replaced by the edges uw and vw for some vertex w not in V (G). The graph obtained from G by subdividing each edge of G exactly once is called the subdivision graph of G and is denoted by S(G). In this paper, we study the nonsplit domination number of subdivision graph. We determine exact values of the nonsplit domination number of subdivision graph for some standard graphs. We also obtain bounds and relationship with other graph theoretic parameters for the γ ns(S(G)).
F. Harary, Graph theory. Reading, MA: Addision-Wesley, 1969.
T. W. Haynes, S. T. Hedetniemi, and P. J. Slater, Fundamentals of domination in graphs. New York, NY; Marcel Dekker, Inc., 1998.
T. W. Haynes, S. M. Hedetniemi, S. T. Hedetniemi, D. P. Jacobs, J. Knisely, and L. C. Van Der Merwe, “Domination subdivision in numbers”, Discussiones mathematicae graph theory, vol. 21, no. 2, pp. 239-253, 2001. doi: 10.7151/dmgt.1147
V. R. Kulli and B. Janakiram, “The nonsplit domination number of a graph”, Indian Journal pure applications mathematical, vol. 31, no. 5, pp. 545-550, May 2000. [On line]. Available: https://bit.ly/3lJtJwi
How to Cite
Copyright (c) 2020 R. Jemimal Chrislight, Y. Therese Sunitha Mary
This work is licensed under a Creative Commons Attribution 4.0 International License.