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An independent dominating set in the complement of a minimum dominating set of a tree

✍ Scribed by Michael A. Henning; Christian Löwenstein; Dieter Rautenbach

Publisher
Elsevier Science
Year
2010
Tongue
English
Weight
267 KB
Volume
23
Category
Article
ISSN
0893-9659

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✦ Synopsis

We prove that for every tree T of order at least 2 and every minimum dominating set D of T which contains at most one endvertex of T , there is an independent dominating set I of T which is disjoint from D. This confirms a recent conjecture of Johnson, Prier, and Walsh.

📜 SIMILAR VOLUMES

Vertices contained in every minimum domi
Vertices contained in every minimum dominating set of a tree
✍ Mynhardt, C. M. 📂 Article 📅 1999 🏛 John Wiley and Sons 🌐 English ⚖ 321 KB

In this article we begin the study of the vertex subsets of a graph G which consist of the vertices contained in all, or in no, respectively, minimum dominating sets of G. We characterize these sets for trees, and also obtain results on the vertices contained in all minimum independent dominating se

Embedding the complement of a minimal bl
Embedding the complement of a minimal blocking set in a projective plane
✍ Lynn Margaret Batten 📂 Article 📅 1984 🏛 Elsevier Science 🌐 English ⚖ 373 KB

A blocking set B in a projective plane z of order n is a subset of T which meets every line but contains no line completely. Hence le)B n I] srz for every line i of 9r.I A blocking set is minimal if it contains no proper blocking set. A blocking set is maximal if it is not properly contained in any