The radius of a triangle-free graph with prescribed edge-connectivity

Abstract

We give an upper bound on the radius of a triangle-free graph in terms of order and edge-connectivity. In particular we prove that if G is a 3-edge-connected triangle-free graph of order n and radius rad(G), then the inequality rad(G)≤3/10n+56/5 holds. Moreover, graphs are constructed to show that the bounds are asymptotically sharp.