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Displaying similar documents to “The forcing steiner number of a graph”

On the forcing geodetic and forcing steiner numbers of a graph

A.P. Santhakumaran, J. John (2011)

Discussiones Mathematicae Graph Theory

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For a connected graph G = (V,E), a set W ⊆ V is called a Steiner set of G if every vertex of G is contained in a Steiner W-tree of G. The Steiner number s(G) of G is the minimum cardinality of its Steiner sets and any Steiner set of cardinality s(G) is a minimum Steiner set of G. For a minimum Steiner set W of G, a subset T ⊆ W is called a forcing subset for W if W is the unique minimum Steiner set containing T. A forcing subset for W of minimum cardinality is a minimum forcing subset...

The Steiner Wiener Index of A Graph

Xueliang Li, Yaping Mao, Ivan Gutman (2016)

Discussiones Mathematicae Graph Theory

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The Wiener index W(G) of a connected graph G, introduced by Wiener in 1947, is defined as W(G) = ∑u,v∈V(G) d(u, v) where dG(u, v) is the distance between vertices u and v of G. The Steiner distance in a graph, introduced by Chartrand et al. in 1989, is a natural generalization of the concept of classical graph distance. For a connected graph G of order at least 2 and S ⊆ V (G), the Steiner distance d(S) of the vertices of S is the minimum size of a connected subgraph whose vertex set...

Constrained Steiner trees in Halin graphs

Guangting Chen, Rainer E. Burkard (2010)

RAIRO - Operations Research

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In this paper, we study the problem of computing a minimum cost Steiner tree subject to a weight constraint in a Halin graph where each edge has a nonnegative integer cost and a nonnegative integer weight. We prove the NP-hardness of this problem and present a fully polynomial time approximation scheme for this NP-hard problem.

Constrained Steiner trees in Halin graphs

Guangting Chen, Rainer E. Burkard (2003)

RAIRO - Operations Research - Recherche Opérationnelle

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In this paper, we study the problem of computing a minimum cost Steiner tree subject to a weight constraint in a Halin graph where each edge has a nonnegative integer cost and a nonnegative integer weight. We prove the NP-hardness of this problem and present a fully polynomial time approximation scheme for this NP-hard problem.