A Note on G(γτss) of Some Graphs

T.Sheeba Helen; T.Nicholas

doi:https://doi.org/10.14445/22315373/IJMTT-V65I4P515

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 65 | Issue 4 | Year 2019 | Article Id. IJMTT-V65I4P515 | DOI : https://doi.org/10.14445/22315373/IJMTT-V65I4P515

A Note on G(γτss) of Some Graphs

T.Sheeba Helen, T.Nicholas

Citation :

T.Sheeba Helen, T.Nicholas, "A Note on G(γτss) of Some Graphs," International Journal of Mathematics Trends and Technology (IJMTT), vol. 65, no. 4, pp. 80-83, 2019. Crossref, https://doi.org/10.14445/22315373/IJMTT-V65I4P515

Abstract

A total dominating set D of graph G = (V, E) is a total strong split dominating set if the induced sub graph < V−D > is totally disconnected with at least two vertices. The total strong split domination number γtss(G) is the minimum cardinality of a total strong split dominating set. In this paper, we introduce the concept 𝛾𝑡𝑠𝑠 − graph of a graph G and define the graph G(𝛾𝑡𝑠𝑠) = (V(𝛾𝑡𝑠𝑠 ), E(𝛾𝑡𝑠𝑠 )) of G to be the graph whose vertices V(𝛾𝑡𝑠𝑠 ) corresponds injectively with the 𝛾𝑡𝑠𝑠 −sets of a graph G and two 𝛾𝑡𝑠𝑠 −sets D1 and D2 form an edge in G(𝛾𝑡𝑠𝑠 ) if there exists a vertex v ∈ D1 and w ∈ D2 such that v is adjacent to w and D1 = D2 – {w} ∪ {v} or equivalently D2 = D1 – {v} ∪ {w}. With this definition, two 𝛾𝑡𝑠𝑠 −sets are said to be adjacent if they differ by one vertex, and the two vertices defining this difference are adjacent in G. We also determine G(𝛾𝑡𝑠𝑠 ) of some graphs.

Keywords

Domination number, total strong split domination number, γτss-graph of a graph.

References

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