Radius, leaf number, connected domination number and minimum degree
P. Mafuta, Simon Mukwembi, Sheunesu Munyira · Quaestiones Mathematicae · 2022
Let G be a simple, connected graph with minimum degree δ, radius r and leaf number L(G). We prove thatWe give similar bounds for triangle-free graphs. Infinite families of graphs are constructed to show that all the bounds here are sharp, except the one for r ≡ 1 modulo 3 in the above piecewise inequality. The results bring to literature new lower bounds on the leaf number and new upper bounds on the radius and connected domination number of a graph. Further, the techniques applied in this paper can be used to improve known asymptotically sharp bounds on the radius and diameter to sharp bounds. We consider simple graphs only.