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The sequence of upper and lower domination, independence and irredundance numbers of a graph

โœ Scribed by E.J. Cockayne; C.M. Mynhardt

Publisher
Elsevier Science
Year
1993
Tongue
English
Weight
803 KB
Volume
122
Category
Article
ISSN
0012-365X

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โœฆ Synopsis

Necessary and sufficient conditions are established for the existence of a graph whose upper and lower domination, independence and irredundance numbers are six given positive integers. This result shows that the only relationships between these six parameters which hold for all graphs and which do not involve other graph theoretical parameters, are already known.

๐Ÿ“œ SIMILAR VOLUMES

On domination and independent domination
On domination and independent domination numbers of a graph
โœ Robert B. Allan; Renu Laskar ๐Ÿ“‚ Article ๐Ÿ“… 1978 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 399 KB

For a graph G, the definitions of doknation number, denoted y(G), and independent domination number, denoted i(G), are given, and the following results are obtained: oorollrrg 1. For any graph G, y(L(G)) = i@(G)), where Z,(G) is the line graph of G. (This $xh!s t.lic rtsult ~(L(T))~i(L(T)), h w ere

The ratio of the irredundance number and
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โœ Zverovich, V. E. ๐Ÿ“‚ Article ๐Ÿ“… 1998 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 96 KB ๐Ÿ‘ 2 views

Let ฮณ(G) and ir(G) denote the domination number and the irredundance number of a graph G, respectively. Allan and Laskar [Proc. 9th Southeast Conf. on Combin., Graph Theory & Comp. (1978) 43-56] and Bollobรกs and Cock- ayne [J. Graph Theory (1979) 241-249] proved independently that ฮณ(G) < 2ir(G) for

The irredundance number and maximum degr
The irredundance number and maximum degree of a graph
โœ B. Bollobรกs; E.J. Cockayne ๐Ÿ“‚ Article ๐Ÿ“… 1984 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 104 KB

A vertex x in a subset X of vertices of an undirected graph is redundant if its dosed neighborhood is contained in the union of closed neighborhoods of vertices of X-{x}. In the context of a communications network, this means that any vertex that may receive communications from X may also be irdorme