## Abstract A maximal independent set of a graph __G__ is an independent set that is not contained properly in any other independent set of __G.__ In this paper, we determine the maximum number of maximal independent sets among all bipartite graphs of order __n__ and the extremal graphs as well as
Polar graphs and maximal independent sets
β Scribed by Vadim V. Lozin; Raffaele Mosca
- Book ID
- 108113471
- Publisher
- Elsevier Science
- Year
- 2006
- Tongue
- English
- Weight
- 201 KB
- Volume
- 306
- Category
- Article
- ISSN
- 0012-365X
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π SIMILAR VOLUMES
Generalizing a theorem of Moon and Moser. we determine the maximum number of maximal independent sets in a connected graph on n vertices for n sufficiently large, e.g., n > 50. = I .32. . .). Example 1.2. Let b, = i(C,), where C,z denotes the circuit of length n. Then b, = 3, 6, = 2, b, = 5, and b,
## Abstract A maximal independent set of a graph __G__ is an independent set that is not contained properly in any other independent set of __G__. Let __i(G)__ denote the number of maximal independent sets of __G__. Here, we prove two conjectures, suggested by P. ErdΓΆs, that the maximum number of m
## Abstract We find the maximum number of maximal independent sets in two families of graphs. The first family consists of all graphs with __n__ vertices and at most __r__ cycles. The second family is all graphs of the first family which are connected and satisfy __n__ββ₯β3__r__. Β© 2006 Wiley Period