Generalised irredundance in graphs: Nordhaus-Gaddum bounds

• Autorzy: Ernest J. Cockayne , Stephen Finbow
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

graph; generalised irredundance; Nordhaus-Gaddum

Kategorie tematyczne

• 05C69: Dominating sets, independent sets, cliques
• 05C55: Generalized Ramsey theory

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2004
• Tom: 24
• Numer: 1
• Strony: 147-160

Daty

wydano

2004

otrzymano

2002-03-20

poprawiono

2003-02-04

Twórcy

autor

Ernest J. Cockayne

• University of Victoria, B.C., Canada V8W 3P4

autor

Stephen Finbow

• University of Victoria, B.C., Canada V8W 3P4

Bibliografia

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Identyfikatory

DOI

10.7151/dmgt.1221