Semitotal Block Double Domination in
Graphs

M. H. Muddebihal; Suhas P. Gade

doi:https://doi.org/10.14445/22315373/IJMTT-V52P561

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 52 | Number 7 | Year 2017 | Article Id. IJMTT-V52P561 | DOI : https://doi.org/10.14445/22315373/IJMTT-V52P561

Semitotal Block Double Domination in Graphs

M. H. Muddebihal, Suhas P. Gade

Citation :

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

Abstract

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.

Keywords

semi total block graph, Dominating set, Strong split dominating set, Double domination.

References

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