• T.Sheeba Helen
• T.Nicholas

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 define the modified γ_tss-graph G〖(γ〗_mtss) = (V〖(γ〗_mtss), E〖(γ〗_mtss)) of G to be the graph whose vertices V〖(γ〗_mtss) corresponds injectively with the γ_tss-sets of a graph G and two γ_tss-sets D1 and D2 form an edge in G〖(γ〗_mtss) if there exists a vertex v ∈ D1 and w ∈ D2 such that D1 = D2 – {w} ∪ {v} and D2 = D1 – {v} ∪ {w}. Thus two γ_tss-sets are said to be adjacent if they differ by one vertex. We also determine G〖(γ〗_mtss) of certain graphs.

Keywords - Domination number, total strong split domination number, γ_tss- graph of a graph, γ_mtss- graph of a graph.

"A Note on G(γ mtss) of Certain Graphs.", International Journal of Emerging Technologies and Innovative Research (www.jetir.org), ISSN:2349-5162, Vol.6, Issue 6, page no.228-232, June 2019, Available :http://www.jetir.org/papers/JETIR1906K22.pdf

"A Note on G(γ mtss) of Certain Graphs.", International Journal of Emerging Technologies and Innovative Research (www.jetir.org | UGC and issn Approved), ISSN:2349-5162, Vol.6, Issue 6, page no. pp228-232, June 2019, Available at : http://www.jetir.org/papers/JETIR1906K22.pdf