Critical concepts in domination
โ Scribed by David P. Sumner
- Publisher
- Elsevier Science
- Year
- 1990
- Tongue
- English
- Weight
- 771 KB
- Volume
- 86
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
The smallest cardinality of any such dominating set is called the domination number of G and is denoted by y(G). The purpose of this paper is to initiate an investigation of those graphs which are critical in the following sense: For each v, u E V(G) with v not adjacent to u, y(G + vu) < y(G). Thus
for any vertex x in G. This work considers properties of k-distance domination-critical graphs and establishes a best possible upper bound on the diameter of a 2-distance domination-critical graph G, that is, d(G) โค 3(ฮณ 2 -1) for ฮณ 2 โฅ 2.
We show that for each k L 4 there exists a connected k-domination critical graph with independent domination number exceeding k, thus disproving a conjecture of Sumner and Blitch ( J Cornbinatorial Theory B 34 (19831, 65-76) in all cases except k = 3.