2 research outputs found
Domination in Benzenoids
A benzenoid is a molecule that can be represented as a graph. This graph is a fragment of the hexagon lattice. A dominating set in a graph is a set of vertices such that each vertex of the graph is either in or adjacent to a vertex in . The domination number of a graph is the size of a minimum dominating set. We will find formulas and bounds for the domination number of various special benzenoids, namely, linear chains , triangulenes , and parallelogram benzenoids . The domination ratio of a graph is , where is the number of vertices of . We will use the preceding results to prove that the domination ratio is no more than for the considered benzenoids. We conjecture that is true for all benzenoids