Results on Split, Non-Split, Inverse Split and Inverse Non-Split Domination Number of Some Special Graphs

T.Aswini; Dr. K.Ameenal Bibi

doi:https://doi.org/10.14445/22315373/IJMTT-V66I8P505

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 66 | Issue 8 | Year 2020 | Article Id. IJMTT-V66I8P505 | DOI : https://doi.org/10.14445/22315373/IJMTT-V66I8P505

Results on Split, Non-Split, Inverse Split and Inverse Non-Split Domination Number of Some Special Graphs

T.Aswini, Dr. K.Ameenal Bibi

Citation :

T.Aswini, Dr. K.Ameenal Bibi, "Results on Split, Non-Split, Inverse Split and Inverse Non-Split Domination Number of Some Special Graphs," International Journal of Mathematics Trends and Technology (IJMTT), vol. 66, no. 8, pp. 34-45, 2020. Crossref, https://doi.org/10.14445/22315373/IJMTT-V66I8P505

Abstract

Let G=(V,E) be a simple, finite, connected and indirected graph. A non-empty subset D ⊆ V is called a dominating set if every vertex in V-D adjacent to at least one vertex in D. The minimum cardinality taken over all the minimal dominating sets of G is called the domination number of G, denoted by γ(G). Let G be the minimum dominating set of G. If V-D contains a dominating set D is called the inverse dominating set of G with respect to D. The inverse dominating number γ'(G) is the minimum cardinality taken over all the minimal inverse dominating set of G. A dominating set D ⊆ V of a graph G is a split(non-split) dominating set if the induced sub graph is disconnected(connected). The split ( not-split) domination number γs(G)[γms(G)] is the minimum cardinality of a split(non-split) dominating set.

Keywords

Dominating set, inverse dominating set, split and non-split domination number, inverse split domination number and inverse non-split domination number.

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