✦ LIBER ✦

Domination critical graphs

✍ Scribed by David P Sumner; Pattie Blitch

Publisher: Elsevier Science
Year: 1983
Tongue: English
Weight: 531 KB
Volume: 34
Category: Article
ISSN: 0095-8956
DOI: 10.1016/0095-8956(83)90007-2

No coin nor oath required. For personal study only.

📜 SIMILAR VOLUMES

✍ David P Sumner; Pattie Blitch 📂 Article 📅 1983 🏛 Elsevier Science 🌐 English ⚖ 531 KB

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

Vertex domination-critical graphs

✍ Jason Fulman; Denis Hanson; Gary Macgillivray 📂 Article 📅 1995 🏛 John Wiley and Sons 🌐 English ⚖ 293 KB

Vertex domination-critical graphs

✍ Robert C. Brigham; Phyllis Z. Chinn; Ronald D. Dutton 📂 Article 📅 1988 🏛 John Wiley and Sons 🌐 English ⚖ 303 KB

Distance domination-critical graphs

✍ Fang Tian; Jun-Ming Xu 📂 Article 📅 2008 🏛 Elsevier Science 🌐 English ⚖ 176 KB

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) ≤ 3(γ 2 -1) for γ 2 ≥ 2.

Local edge domination critical graphs

✍ Michael A. Henning; Ortrud R. Oellermann; Henda C. Swart 📂 Article 📅 1996 🏛 Elsevier Science 🌐 English ⚖ 521 KB

Sumner and Blitch defined a graph G to be k-y-critical if 7(G) = k and 7(G + uv) = k -1 for each pair u, v of nonadjacent vertices of G. We define a graph to be k-( 7,d)-critical if 7(G) = k and 7(G + uv) = k -I for each pair u, v of nonadjacent vertices of G that are at distance at most d apart. Th

Domination critical graphs with higher i

Domination critical graphs with higher independent domination numbers

✍ Ao, S.; Cockayne, E.J.; MacGillivray, G.; Mynhardt, C.M. 📂 Article 📅 1996 🏛 John Wiley and Sons 🌐 English ⚖ 348 KB 👁 2 views

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.