International Journal of Mathematics Trends and Technology
Volume 52 | Number 7 | Year 2017 | Article Id. IJMTT-V52P561 | DOI : https://doi.org/10.14445/22315373/IJMTT-V52P561
For any graph 𝐺 = (𝑉, 𝐸), the semitotal block graph 𝑇𝑏 𝐺 = 𝐻, whose set of vertices is the union of the set of vertices and block of 𝐺 and in which two vertices are adjacent if and if the corresponding vertices of 𝐺 are adjacent or the corresponding members are incident in 𝐺. A subset 𝐷 𝑑 of 𝑉[𝑇𝑏 𝐺 ] is double dominating set of 𝑇𝑏 𝐺 if for every vertex 𝑣 ∈ 𝑉 𝑇𝑏 𝐺 , 𝑁[𝑣] ∩ 𝐷 𝑑 ≥ 2, that is 𝑣 is in 𝐷 𝑑 and has at least one neighbor in 𝐷 𝑑 or 𝑣 is in 𝑉 𝑇𝑏 𝐺 −𝐷 𝑑 and has at least two neighbors in 𝐷 𝑑 . The semitotal block dominating number 𝛾𝑑𝑑𝑡𝑏 (𝐺) is a minimum cardinality of the semitotal block double dominating set of 𝐺 and is denoted by 𝛾𝑑𝑑𝑡𝑏 (𝐺). In this paper, we establish some sharp bounds for 𝛾𝑑𝑑𝑡𝑏 (𝐺). Also some upper and lower bounds on 𝛾𝑑𝑑𝑡𝑏 (𝐺) in terms of elements of 𝐺 and other dominating parameters of 𝐺 are obtained.
[1] G.Chartrand and Lesniak, Graphs and Digraphs, third edition, Chapman and Hall, London, (1996).
[2] F. Harary, Graph Theory, Addison-Wesley, Reading Mass (1974).
[3] T.W. Hyness, S.T. Hedetniemi and P.J. Slater, Fundamentals of Domination in Graph, Marcell Dekker, INC- (1998).
[4] V.R. Kulli, The semitotal-block graph and the Total-block graph of a graph, Indian journal of Pure and Applied Mathematics Vol. 7, No.6 (June 1976), 625-630.
[5] V.R. Kulli, Theory of domination in Graphs, Vishva International Publications, (2010).
M. H. Muddebihal, Suhas P. Gade, "Semitotal Block Double Domination in Graphs," International Journal of Mathematics Trends and Technology (IJMTT), vol. 52, no. 7, pp. 435-438, 2017. Crossref, https://doi.org/10.14445/22315373/IJMTT-V52P561
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