Connected Total Dominating Sets and Connected Total Domination Polynomials of Square of Paths

A. Vijayan; T. Anitha Baby

doi:https://doi.org/10.14445/22315373/IJMTT-V11P507

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 11 | Number 1 | Year 2014 | Article Id. IJMTT-V11P507 | DOI : https://doi.org/10.14445/22315373/IJMTT-V11P507

Connected Total Dominating Sets and Connected Total Domination Polynomials of Square of Paths

A. Vijayan, T. Anitha Baby

Citation :

A. Vijayan, T. Anitha Baby, "Connected Total Dominating Sets and Connected Total Domination Polynomials of Square of Paths," International Journal of Mathematics Trends and Technology (IJMTT), vol. 11, no. 1, pp. 56-63, 2014. Crossref, https://doi.org/10.14445/22315373/IJMTT-V11P507

Abstract

Let G be a simple connected graph of order n. Let Dct(G, i) be the family of connected total dominating sets in G with cardinality i. The polynomial Dct (G, x) = nΣdcti=γct(G) (G, i) xi is called the connected total domination polynomial of G. In this paper, we obtain a recursive formula for dct (Pn2 , i). Using this recursive formula, we construct the connected total domination polynomial Dct (Pn2 , x) =nΣi=[n-3/2] dct( Pn2, i) xi , where dct (Pn2 , i) is the number of connected total dominating sets of of cardinality i and some properties of this polynomial have been studied.

Keywords

Square of Path, connected total dominating set, connected total domination number, connected total domination polynomial.

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