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An upper bound on the 2-outer-independent domination number of a tree

✍ Scribed by Marcin Krzywkowski

Book ID
116389935
Publisher
Elsevier Science
Year
2011
Tongue
English
Weight
121 KB
Volume
349
Category
Article
ISSN
1631-073X

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✍ Liang Sun; Jianfang Wang πŸ“‚ Article πŸ“… 1999 πŸ› Elsevier Science 🌐 English βš– 87 KB

Let G be a simple graph of order n and minimum degree $. The independent domination number i(G) is defined to be the minimum cardinality among all maximal independent sets of vertices of G. In this paper, we show that i(G) n+2$&2 -n$. Thus a conjecture of Favaron is settled in the affirmative.

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✍ E. J. Cockayne; B. Gamble; B. Shepherd πŸ“‚ Article πŸ“… 1985 πŸ› John Wiley and Sons 🌐 English βš– 82 KB πŸ‘ 2 views

The kdomination number of a graph G, y k ( G ) , is the least cardinality of a set U of verticies such that any other vertex is adjacent to at least k vertices of U. We prove that if each vertex has degree at least k. then YAG) 5 kp/(k + 1).