Counting dominating sets and related structures in graphs
نویسندگان
چکیده
منابع مشابه
Counting dominating sets and related structures in graphs
We first consider some problems related to the maximum number of dominating (or strong dominating) sets in a regular graph. Our techniques, centered around Shearer’s entropy lemma, extend to a reasonably broad class of graph parameters enumerating vertex colorings that satisfy conditions on the multiset of colors appearing in neighborhoods (either open or closed). Dominating sets and strong dom...
متن کاملStrength of strongest dominating sets in fuzzy graphs
A set S of vertices in a graph G=(V,E) is a dominating set ofG if every vertex of V-S is adjacent to some vertex of S.For an integer k≥1, a set S of vertices is a k-step dominating set if any vertex of $G$ is at distance k from somevertex of S. In this paper, using membership values of vertices and edges in fuzzy graphs, we introduce the concepts of strength of strongestdominating set as well a...
متن کاملCounting Minimum Weighted Dominating Sets
We show how to count all minimumweighted dominating sets of a graph on n vertices in timeO(1.5535).
متن کاملDominating sets in directed graphs
We consider the problem of incrementally computing a minimal dominating set of a directed graph after the insertion or deletion of a set of arcs. Earlier results have either focused on the study of the properties that minimum (not minimal) dominating sets preserved or lacked to investigate which update affects a minimal dominating set and in what ways. In this paper, we first show how to increm...
متن کاملDominating Sets in Planar Graphs
Motivated by an application to unstructured multigrid calculations, we consider the problem of asymptotically minimizing the size of dominating sets in triangulated planar graphs. Speci cally, we wish to nd the smallest such that, for n su ciently large, every n-vertex planar graph contains a dominating set of size at most n. We prove that 1 4 13 , and we conjecture that = 14 . For triangulated...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2016
ISSN: 0012-365X
DOI: 10.1016/j.disc.2015.12.011