The metric dimension, the partition dimension and indices of graphs

We study several problems in the extremal graph theory related to the study of distances in graphs. The first research problem is to find exact values or bounds for the metric dimension of various classes of graphs. The second problem is to determine or bound the partition dimension of graphs. The third problem is to give values or bounds for graph indices in terms of important parameters of graphs. Since group theory techniques have not been used much in this field before, we would like to obtain significant results using our group theory knowledge.