Domination in functigraphs

• Autorzy: Linda Eroh , Ralucca Gera , Cong X. Kang , Craig E. Larson , Eunjeong Yi
• Języki publikacji: EN

Abstrakty

EN

Let G₁ and G₂ be disjoint copies of a graph G, and let f:V(G₁) → V(G₂) be a function. Then a functigraph C(G,f) = (V,E) has the vertex set V = V(G₁) ∪ V(G₂) and the edge set E = E(G₁) ∪ E(G₂) ∪ {uv | u ∈ V(G₁), v ∈ V(G₂),v = f(u)}. A functigraph is a generalization of a permutation graph (also known as a generalized prism) in the sense of Chartrand and Harary. In this paper, we study domination in functigraphs. Let γ(G) denote the domination number of G. It is readily seen that γ(G) ≤ γ(C(G,f)) ≤ 2 γ(G). We investigate for graphs generally, and for cycles in great detail, the functions which achieve the upper and lower bounds, as well as the realization of the intermediate values.

Słowa kluczowe

EN

domination; permutation graphs; generalized prisms; functigraphs

Kategorie tematyczne

• 05C38: Paths and cycles
• 05C69: Dominating sets, independent sets, cliques

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2012
• Tom: 32
• Numer: 2
• Strony: 299-319

Daty

wydano

2012

otrzymano

2010-07-12

poprawiono

2011-06-06

zaakceptowano

2011-06-06

Twórcy

autor

Linda Eroh

• Department of Mathematics, University of Wisconsin Oshkosh, Oshkosh, WI 54901, USA

autor

Ralucca Gera

• Department of Applied Mathematics, Naval Postgraduate School, Monterey, CA 93943, USA

autor

Cong X. Kang

• Department of General Academics, Texas A&M University at Galveston, Galveston, TX 77553, USA

autor

Craig E. Larson

• Department of Mathematics and Applied Mathematics, Virginia Commonwealth University, Richmond, VA 23284, USA

autor

Eunjeong Yi

• Department of General Academics, Texas A&M University at Galveston, Galveston, TX 77553, USA

Bibliografia

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Identyfikatory

DOI

10.7151/dmgt.1600