Abstract
In 1989, Chartrand, Oellermann, Tian and Zou introduced the Steiner distance for graphs. This is a natural generalization of the classical graph distance concept. Let Γ be a connected graph of order at least 2, and S\V(Γ). Then, the minimum size among all the connected subgraphs whose vertex sets contain S is the Steiner distancedΓ(S) among the vertices of S. The Steiner k-eccentricity ek(v) of a vertex v of Γ is defined by ek(v)=max{dΓ(S)|S\V(Γ),|S|=k,andv∈S}, where n and k are two integers, with 2≤k≤n, and the Steiner k-diameter of Γ is defined by sdiamk(Γ)=max{ek(v)|v∈V(Γ)}. In this paper, we present an algorithm to derive the Steiner distance of a graph; in addition, we obtain a relationship between the Steiner k-diameter of a graph and its line graph. We study various properties of the Steiner diameter through a combinatorial approach. Moreover, we characterize graph Γ when sdiamk(Γ) is given, and we determine sdiamk(Γ) for some special graphs. We also discuss some of the applications of Steiner diameter, including one in education networks.
Subject
General Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)
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