- Tytuł:
- Generalised irredundance in graphs: Nordhaus-Gaddum bounds
- Autorzy:
-
Cockayne, Ernest
Finbow, Stephen - Powiązania:
- https://bibliotekanauki.pl/articles/744461.pdf
- Data publikacji:
- 2004
- Wydawca:
- Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
- Tematy:
-
graph
generalised irredundance
Nordhaus-Gaddum - Opis:
- For each vertex s of the vertex subset S of a simple graph G, we define Boolean variables p = p(s,S), q = q(s,S) and r = r(s,S) which measure existence of three kinds of S-private neighbours (S-pns) of s. A 3-variable Boolean function f = f(p,q,r) may be considered as a compound existence property of S-pns. The subset S is called an f-set of G if f = 1 for all s ∈ S and the class of f-sets of G is denoted by $Ω_f(G)$. Only 64 Boolean functions f can produce different classes $Ω_f(G)$, special cases of which include the independent sets, irredundant sets, open irredundant sets and CO-irredundant sets of G. Let $Q_f(G)$ be the maximum cardinality of an f-set of G. For each of the 64 functions f, we establish sharp upper bounds for the sum $Q_f(G) + Q_f(G̅)$ and the product $Q_f(G)Q_f(G̅)$ in terms of n, the order of G.
- Źródło:
-
Discussiones Mathematicae Graph Theory; 2004, 24, 1; 147-160
2083-5892 - Pojawia się w:
- Discussiones Mathematicae Graph Theory
- Dostawca treści:
- Biblioteka Nauki
Artykuł