On the radius of graphs

  title={On the radius of graphs},
  author={Jochen Harant and Hansjoachim Walther},
  journal={J. Comb. Theory, Ser. B},
An Upper Bound on the Radius of a 3-Edge-Connected Graph
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.
An Upper Bound on the Radius of a 3-Vertex-Connected C4-Free Graph
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 G is a 3-connected graph with radius r , then r ≤ | V ( G ) | +15 4 .
Minimum size of a graph or digraph of given radius
The radius of k-connected planar graphs with bounded faces
Order and radius of (2k−1)-connected graphs
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.
On smallest $3$-polytopes of given graph radius
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?
An Upper Bound on the Diameter of a 3-Edge-Connected C4-Free Graph
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
Aspects of distance measures in graphs.
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


On the depth of a planar graph
Graph theory