# DMGT

ISSN 1234-3099 (print version)

ISSN 2083-5892 (electronic version)

# IMPACT FACTOR 2018: 0.741

SCImago Journal Rank (SJR) 2018: 0.763

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# Discussiones Mathematicae Graph Theory

## Domination in Functigraphs

 Linda Eroh1, Ralucca Gera2, Cong X. Kang 3, Craig E. Larson4 and Eunjeong Yi3 1 Department of Mathematics University of Wisconsin Oshkosh Oshkosh, WI 54901, USA 2 Department of Applied Mathematics Naval Postgraduate School

## Abstract

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.

Keywords: domination, permutation graphs, generalized prisms, functigraphs

2010 Mathematics Subject Classification: 05C69, 05C38.

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