## Abstract A graph __G__ is 3βdomination critical if its domination number Ξ³ is 3 and the addition of any edge decreases Ξ³ by 1. Let __G__ be a 3βconnected 3βdomination critical graph of order __n__. In this paper, we show that there is a path of length at least __n__β2 between any two distinct ve
Connected domination critical graphs
β Scribed by Xue-Gang Chen; Liang Sun; De-Xiang Ma
- Publisher
- Elsevier Science
- Year
- 2004
- Tongue
- English
- Weight
- 339 KB
- Volume
- 17
- Category
- Article
- ISSN
- 0893-9659
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π 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) β€ 3(Ξ³ 2 -1) for Ξ³ 2 β₯ 2.