Bounds on the Steiner radius of a graph.

For a connected graph G of order p and a set S ⊆ V (G) , the Steiner distance of S is the minimum number of edges in a connected subgraph of G containing S. If n is an integer, 2 ≤ n ≤ p and a vertex v ∈ V (G) , the Steiner n -eccentricity of a vertex v of G , ex n (v) , is the maximum Steiner distance of all n -subsets of V (G) containing v. The Steiner n -radius of G , rad n (G) , is the minimum Steiner n -eccentricities of all vertices in G. We give bounds on rad n (G) in terms of the order of G and the minimum degree of G for all graphs and for graphs that contain no triangles. We shall also investigate the relation between the n -radius of a graph G and its complement Ḡ. [ABSTRACT FROM AUTHOR]