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.
Received: 30 June 2019 / Revised: 26 July 2019 / Accepted: 27 July 2019 / Published: 30 July 2019
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For a graph
-graph of G
, is the graph whose vertex set is the collection of minimum dominating sets, or
-sets of G
, and two
-sets are adjacent in
if they differ by a single vertex and the two different vertices are adjacent in G
. In this paper, we consider
-graphs of trees. We develop an algorithm for determining the
-graph of a tree, characterize which trees are
-graphs of trees, and further comment on the structure of
-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.
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MDPI and ACS Style
Finbow, S.; van Bommel, C.M. γ-Graphs of Trees. Algorithms 2019, 12, 153.
Finbow S, van Bommel CM. γ-Graphs of Trees. Algorithms. 2019; 12(8):153.
Finbow, Stephen; van Bommel, Christopher M. 2019. "γ-Graphs of Trees." Algorithms 12, no. 8: 153.
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