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- W4256367020 abstract "A dominating set for a graph G = (V,E) is a subset of vertices V′ ⊆ V such that for all v E V − V′ there exists some u E V′ for which {v, u} E E. The domination number of G is the size of its smallest dominating set(s). We show that for almost all connected graphs with minimum degree at least 2 and q edges, the domination number is bounded by (q + 1)/3. From this we derive exact lower bounds for the number of edges of a connected graph with minimum degree at least 2 and a given domination number. We also generalize the bound to k-restricted domination numbers; these measure how many vertices are necessary to dominate a graph if an arbitrary set of k vertices must be incluced in the dominating set. © 1997 John Wiley & Sons, Inc. J Graph Theory 25: 139–152, 1997" @default.
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- W4256367020 date "1997-06-01" @default.
- W4256367020 modified "2023-09-27" @default.
- W4256367020 title "Bounds related to domination in graphs with minimum degree two" @default.
- W4256367020 doi "https://doi.org/10.1002/(sici)1097-0118(199706)25:2<139::aid-jgt6>3.3.co;2-p" @default.
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