Open AccessReconfiguring minimum dominating sets: the γ-graph of a tree
Author(s) -
M. Edwards,
Gary MacGillivray,
Shahla Nasserasr
Publication year - 2018
Publication title -
discussiones mathematicae graph theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.476
H-Index - 19
eISSN - 2083-5892
pISSN - 1234-3099
DOI - 10.7151/dmgt.2044
Subject(s) - mathematics , dominating set , combinatorics , graph , tree (set theory) , discrete mathematics , vertex (graph theory)
We consider γ-graphs, which are reconfiguration graphs of the minimum dominating sets of a graph G. We answer three open questions about γ- graphs of trees by providing upper bounds on the maximum degree, the diameter, and the number of minimum dominating sets. The latter gives an upper bound on the order of the γ-graph.
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