The Split Domination, Inverse Domination and Equitable Domination in the Middle and the Central graphs of the Path and the Cycle graphs

K. Ameenal Bibi; P.Rajakumari

doi:https://doi.org/10.14445/22315373/IJMTT-V49P523

International Journal of Mathematics Trends and Technology

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Volume 49 | Number 3 | Year 2017 | Article Id. IJMTT-V49P523 | DOI : https://doi.org/10.14445/22315373/IJMTT-V49P523

The Split Domination, Inverse Domination and Equitable Domination in the Middle and the Central graphs of the Path and the Cycle graphs

K. Ameenal Bibi, P.Rajakumari

Abstract

Let G=(V,E) be a simple, finite, connected and undirected graph. A non- empty subset D of V(G) in a graph G=(V,E) is a dominating set if every vertex in V-D is adjacent to atleast one vertex in D. The domination number γ(G) of G is the minimum cardinality of a minimal dominating set of G. A non-empty subset D of V(G) is called an equitable dominating set of a graph G if for every , there exists a vertex such that and . The minimum cardinality of such a minimal dominating set is denoted by γe(G) and is called an equitable domination number of G. A dominating set D of graph G is called a split dominating set, if the induced subgraph is disconnected. Let denote the greatest integer not greater than and denote the least integer not less than x . In this paper, we investigated the split, inverse and equitable domination number of the middle and the central graphs of the path Pn and the cycle Cn.

Keywords

Dominating set, Domination number, Split domination, Inverse domination, equitable domination, middle graph, Central graph, Path Graph and Cycle Graph.

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Citation :

K. Ameenal Bibi, P.Rajakumari, "The Split Domination, Inverse Domination and Equitable Domination in the Middle and the Central graphs of the Path and the Cycle graphs," International Journal of Mathematics Trends and Technology (IJMTT), vol. 49, no. 3, pp. 168-173, 2017. Crossref, https://doi.org/10.14445/22315373/IJMTT-V49P523