k-domination and total k-domination numbers in catacondensed hexagonal systems

Abstract

In this paper we study the k-domination and total k-domination numbers of catacondensed hexagonal systems. More precisely, we give the value of the total domination number, we find upper and lower bounds for the 2-domination number and the total 2-domination number, characterizing the catacondensed hexagonal systems which attain these bounds, and we give the value of the 3-domination number for any catacondensed hexagonal system with a given number of hexagons. These results complete the study of k-domination and total k-domination of catacondensed hexagonal systems for all possible values of k.

Keywords

• domination
• k-domination
• hexagonal systems
• catacondensed hexagonal systems