Affiliation:
1. Department of Mathematical Sciences, University of Malawi, Malawi
2. Combinatorial Mathematics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung and the Collaborative Research Center for Graph Theory and Combinatorics, Indonesia
Abstract
For a connected graph [Formula: see text] of order [Formula: see text] and a set [Formula: see text], the Steiner distance of [Formula: see text] is the minimum number of edges in a connected subgraph of [Formula: see text] containing [Formula: see text]. If [Formula: see text] is an integer, [Formula: see text] and a vertex [Formula: see text], the Steiner [Formula: see text]-eccentricity of a vertex [Formula: see text] of [Formula: see text], [Formula: see text], is the maximum Steiner distance of all [Formula: see text]-subsets of [Formula: see text] containing [Formula: see text]. The Steiner [Formula: see text]-radius of [Formula: see text], [Formula: see text], is the minimum Steiner [Formula: see text]-eccentricities of all vertices in [Formula: see text]. We give bounds on [Formula: see text] in terms of the order of [Formula: see text] and the minimum degree of [Formula: see text] for all graphs and for graphs that contain no triangles. We shall also investigate the relation between the [Formula: see text]-radius of a graph [Formula: see text] and its complement [Formula: see text].
Publisher
World Scientific Pub Co Pte Ltd
Subject
Discrete Mathematics and Combinatorics