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Vertex domination-critical graphs

✍ Scribed by Jason Fulman; Denis Hanson; Gary Macgillivray

Publisher: John Wiley and Sons
Year: 1995
Tongue: English
Weight: 293 KB
Volume: 25
Category: Article
ISSN: 0028-3045
DOI: 10.1002/net.3230250203

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📜 SIMILAR VOLUMES

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

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.

Hamiltonian properties of domination-cri

Hamiltonian properties of domination-critical graphs

✍ Ewa Wojcicka 📂 Article 📅 1990 🏛 John Wiley and Sons 🌐 English ⚖ 445 KB

## Abstract In this paper we show that every connected, 3‐γ‐critical graph on more than 6 vertices has a Hamiltonian path.

Minimum vertex-diameter-2-critical graph

Minimum vertex-diameter-2-critical graphs

✍ Ya-Chen Chen; Zoltán Füredi 📂 Article 📅 2005 🏛 John Wiley and Sons 🌐 English ⚖ 182 KB 👁 1 views

## Abstract We prove that the minimum number of edges in a vertex‐diameter‐2‐critical graph on __n__ ≥ 23 vertices is (5__n__ − 17)/2 if __n__ is odd, and is (5__n__/2) − 7 if __n__ is even. © 2005 Wiley Periodicals, Inc. J Graph Theory

Vertex criticality for upper domination

Vertex criticality for upper domination and irredundance

✍ P. J. P. Grobler; C. M. Mynhardt 📂 Article 📅 2001 🏛 John Wiley and Sons 🌐 English ⚖ 104 KB

## Abstract Let π be any of the domination parameters __ir__ γ, __i__, β, Γ or __IR__. The graph __G__ is π‐__critical__ (π^+^‐__critical__) if the removal of any vertex of __G__ causes π(__G__) to decrease (increase). We show that the classes of __IR__‐critical and Γ‐critical graphs coincide, and

On vertex critical graphs with prescribe

On vertex critical graphs with prescribed diameter

✍ L. Caccetta; S. EL-Batanouny; J. Huang 📂 Article 📅 2003 🏛 John Wiley and Sons 🌐 English ⚖ 167 KB 👁 1 views

## Abstract Let __G__ be connected simple graph with diameter __d__(__G__). __G__ is said __v__^+^‐critical if __d__(__G__−__v__) is greater than __d__(__G__) for every vertex __v__ of __G__. Let D′ = max {__d__(__G__−__v__) : __v__ ∈ __V__(__G__)}. Boals et al. [Congressus Numerantium 72 (1990), 1