Extremal Ratio Questions in Binary Trees

The values of various important topological indices, when considered as a local function associated with vertices of trees, tend to achieve the extrema at leaves or in the “middle' of a tree. To consider the extremal ratios of such values turns out to be a much more difficult question than general extremal problems. Such problems were considered for the distance function and number of subtrees in general trees. We examine the same questions on binary trees as an effort to generalize this study. Some new results will be provided along with many questions.