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γ-Graphs of Trees

Department of Mathematics and Statistics, St. Francis Xavier University, Antigonish, NS B2G2W5, Canada
Department of Combinatorics and Optimization, University of Waterloo, Waterloo, ON N2L 3G1, Canada
Author to whom correspondence should be addressed.
Algorithms 2019, 12(8), 153;
Received: 30 June 2019 / Revised: 26 July 2019 / Accepted: 27 July 2019 / Published: 30 July 2019
PDF [320 KB, uploaded 30 July 2019]


For a graph G = ( V , E ) , the γ -graph of G, denoted G ( γ ) = ( V ( γ ) , E ( γ ) ) , is the graph whose vertex set is the collection of minimum dominating sets, or γ -sets of G, and two γ -sets are adjacent in G ( γ ) if they differ by a single vertex and the two different vertices are adjacent in G. In this paper, we consider γ -graphs of trees. We develop an algorithm for determining the γ -graph of a tree, characterize which trees are γ -graphs of trees, and further comment on the structure of γ -graphs of trees and its connections with Cartesian product graphs, the set of graphs which can be obtained from the Cartesian product of graphs of order at least two. View Full-Text
Keywords: domination; gamma graphs; reconfiguration domination; gamma graphs; reconfiguration

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Finbow, S.; van Bommel, C.M. γ-Graphs of Trees. Algorithms 2019, 12, 153.

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