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The ratio of the irredundance and domination number of a graph

โœ Scribed by Lutz Volkmann


Book ID
108316224
Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
359 KB
Volume
178
Category
Article
ISSN
0012-365X

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The ratio of the irredundance number and
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

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The vertices of the queem;' graph {~, are the squares of an n ร— n chessboard and two squares are adjacent ifa queen placed on one covers the other. It is shown that the domination num;~'r of Q. is at most 31n/54 + O(1), that Q. possesses minimal dominating sets of cardina~tty 5n/2 -O(l) and that the

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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

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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