Let G be a 3-edge-connected graph of order n and radius rad(G). Then the inequality rad(G) ≤ 1 3 n+ 17 3 is proved. Moreover, graphs are constructed to show that the bound is asymptotically sharp.

We show that if is a 3-vertex-connected - free graph of order and radius , then the inequality holds. Moreover, graphs are constructed to show that the bounds are asymptotically sharp.

We show that if k is an integer with k ≥ 3a ndG is a (2k − 1)- connected graph with radius r ,t hen|V (G) |≥ 2kr − 2k − 2. AMS 2000 Mathematics Subject Classification. 05C12.

The 3 -polytopes are planar, 3 -connected graphs. A classical question is, for r ≥ 3 , is the 2( r − 1) -gonal prism K 2 × C 2( r − 1) the unique 3 -polytope of graph radius r and smallest size?… Expand

We give an upper bound on the diameter of a 3-edge-connected C4-free graph in terms of order. In particular we show that if G is a 3-edge-connected C4 free graph of order n, and diameter d, then the… Expand

In this thesis we investigate bounds on distance measures, namely, Steiner diameter and radius, in terms of other graph parameters. The thesis consists of four chapters. In Chapter 1, we de ne the… Expand