# The forcing steiner number of a graph

Discussiones Mathematicae Graph Theory (2011)

- Volume: 31, Issue: 1, page 171-181
- ISSN: 2083-5892

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topA.P. Santhakumaran, and J. John. "The forcing steiner number of a graph." Discussiones Mathematicae Graph Theory 31.1 (2011): 171-181. <http://eudml.org/doc/270960>.

@article{A2011,

abstract = {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 of W. The forcing Steiner number of W, denoted by fₛ(W), is the cardinality of a minimum forcing subset of W. The forcing Steiner number of G, denoted by fₛ(G), is fₛ(G) = min\{fₛ(W)\}, where the minimum is taken over all minimum Steiner sets W in G. Some general properties satisfied by this concept are studied. The forcing Steiner numbers of certain classes of graphs are determined. It is shown for every pair a, b of integers with 0 ≤ a < b, b ≥ 2, there exists a connected graph G such that fₛ(G) = a and s(G) = b.},

author = {A.P. Santhakumaran, J. John},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {geodetic number; Steiner number; forcing geodetic number; forcing Steiner number},

language = {eng},

number = {1},

pages = {171-181},

title = {The forcing steiner number of a graph},

url = {http://eudml.org/doc/270960},

volume = {31},

year = {2011},

}

TY - JOUR

AU - A.P. Santhakumaran

AU - J. John

TI - The forcing steiner number of a graph

JO - Discussiones Mathematicae Graph Theory

PY - 2011

VL - 31

IS - 1

SP - 171

EP - 181

AB - 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 of W. The forcing Steiner number of W, denoted by fₛ(W), is the cardinality of a minimum forcing subset of W. The forcing Steiner number of G, denoted by fₛ(G), is fₛ(G) = min{fₛ(W)}, where the minimum is taken over all minimum Steiner sets W in G. Some general properties satisfied by this concept are studied. The forcing Steiner numbers of certain classes of graphs are determined. It is shown for every pair a, b of integers with 0 ≤ a < b, b ≥ 2, there exists a connected graph G such that fₛ(G) = a and s(G) = b.

LA - eng

KW - geodetic number; Steiner number; forcing geodetic number; forcing Steiner number

UR - http://eudml.org/doc/270960

ER -

## References

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