Total and Double Total Domination Number on Hexagonal Grid

Abstract

In this paper, we determine the upper and lower bound for the total domination number and exact values and the upper bound for the double-total domination number on hexagonal grid H m , n with m hexagons in a row and n hexagons in a column. Further, we explore the ratio between the total domination number and the number of vertices of H m , n when m and n tend to infinity.

Keywords

• total domination number
• double-total domination number
• hexagonal grid
• molecular graph