Maximum graphs with a unique minimum dominating set
نویسندگان
چکیده
منابع مشابه
Maximum graphs with a unique minimum dominating set
We present a conjecture on the maximum number of edges of a graph that has a unique minimum dominating set. We verify our conjecture for some special cases and prove a weakened version of this conjecture in general. c © 2002 Elsevier Science B.V. All rights reserved.
متن کاملMaximum graphs with unique minimum dominating set of size two
We prove that the maximum number of edges of a graph of order n which has a unique minimum dominating set of size two is bounded above by ( n−2 2 ) . As a corollary to this result, we prove a conjecture by Fischermann, Rautenbach and Volkmann that the maximum number of edges of a graph which has a unique minimum dominating set of size two is ( n−2 2 ) .
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In this paper, we consider graphs having a unique minimum independent dominating set. We first discuss the effects of deleting a vertex, or the closed neighborhood of a vertex, from such graphs. We then discuss five operations which, in certain circumstances, can be used to combine two graphs, each having a unique minimum independent dominating set, to produce a new graph also having a unique m...
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A dominating set for a graph G is a subset D of V such that every vertex not in D is adjacent to at least one member of D. This paper deals with some of the graphs having unique minimum dominating sets. We also find a unique minimum dominating sets for block graphs and maximum graphs.
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2003
ISSN: 0012-365X
DOI: 10.1016/s0012-365x(02)00670-2