- Tytuł:
- The forcing steiner number of a graph
- Autorzy:
-
Santhakumaran, A.
John, J. - Powiązania:
- https://bibliotekanauki.pl/articles/743843.pdf
- Data publikacji:
- 2011
- Wydawca:
- Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
- Tematy:
-
geodetic number
Steiner number
forcing geodetic number
forcing Steiner number - Opis:
- 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.
- Źródło:
-
Discussiones Mathematicae Graph Theory; 2011, 31, 1; 171-181
2083-5892 - Pojawia się w:
- Discussiones Mathematicae Graph Theory
- Dostawca treści:
- Biblioteka Nauki
Artykuł