Affiliation:
1. Department of Mathematics, Government College of Engineering, Tirunelveli-627 007, India
Abstract
A total Steiner set of [Formula: see text] is a Steiner set [Formula: see text] such that the subgraph [Formula: see text] induced by [Formula: see text] has no isolated vertex. The minimum cardinality of a total Steiner set of [Formula: see text] is the total Steiner number of [Formula: see text] and is denoted by [Formula: see text]. Some general properties satisfied by this concept are studied. Connected graphs of order [Formula: see text] with total Steiner number 2 or 3 are characterized. We partially characterized classes of graphs of order [Formula: see text] with total Steiner number equal to [Formula: see text] or [Formula: see text] or [Formula: see text]. It is shown that [Formula: see text]. It is shown that for every pair k, p of integers with [Formula: see text], there exists a connected graph [Formula: see text] of order [Formula: see text] such that [Formula: see text]. Also, it is shown that for every positive integer [Formula: see text], [Formula: see text] and [Formula: see text] with [Formula: see text], there exists a connected graph [Formula: see text] of order [Formula: see text] such that [Formula: see text] and [Formula: see text].
Publisher
World Scientific Pub Co Pte Lt
Subject
Discrete Mathematics and Combinatorics
Cited by
3 articles.
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1. The total edge Steiner number of a graph;Annals of the University of Craiova - Mathematics and Computer Science Series;2021-06-30
2. On the vertex monophonic, vertex geodetic and vertex Steiner numbers of graphs;Asian-European Journal of Mathematics;2021-02-05
3. THE VERTEX STEINER NUMBER OF A GRAPH;TRANS COMB;2020