Maximizing the number of independent subsets over trees with bounded degree
نویسندگان
چکیده
منابع مشابه
Maximizing the number of independent subsets over trees with bounded degree
The number of independent vertex subsets is a graph parameter that is, apart from its purely mathematical importance, of interest in mathematical chemistry. In particular, the problem of maximizing or minimizing the number of independent vertex subsets within a given class of graphs has already been investigated by many authors. In view of the applications of this graph parameter, trees of rest...
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The number of independent vertex subsets is a graph parameter that is, apart from its purely mathematical importance, of interest in mathematical chemistry. In particular, the problem of maximizing or minimizing the number of independent vertex subsets within a given class of graphs has been investigated in many papers. In view of the applications of this graph parameter, trees of restricted de...
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The number of independent vertex subsets is a graph parameter that is, apart from its purely mathematical importance, of interest in mathematical chemistry. In particular, the problem of maximizing or minimizing the number of independent vertex subsets within a given class of graphs has been investigated in many papers. In view of the applications of this graph parameter, trees of restricted de...
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A Roman dominating function (RDF) on a graph G=(V,E) is a function f : V → {0, 1, 2} such that every vertex u for which f(u)=0 is adjacent to at least one vertex v for which f(v)=2. An RDF f is calledan outer independent Roman dominating function (OIRDF) if the set ofvertices assigned a 0 under f is an independent set. The weight of anOIRDF is the sum of its function values over ...
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Given a set of n real numbers, if the sum of the elements of every subset of size larger than k is negative, what is the maximum number of subsets of nonnegative sum? In this note we show that the answer is (n−1 k−1 ) + (n−1 k−2 ) + · · ·+ (n−1 0 ) + 1, settling a problem of Tsukerman. We provide two proofs; the first establishes and applies a weighted version of Hall’s theorem, and the second ...
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ژورنال
عنوان ژورنال: Journal of Graph Theory
سال: 2008
ISSN: 0364-9024,1097-0118
DOI: 10.1002/jgt.20294