On Graphs Having Maximal Independent Sets of ExactlytDistinct Cardinalities
β Scribed by Bert L. Hartnell, Douglas F. Rall
- Book ID
- 120788683
- Publisher
- Springer Japan
- Year
- 2012
- Tongue
- English
- Weight
- 164 KB
- Volume
- 29
- Category
- Article
- ISSN
- 0911-0119
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## 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
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,
In this paper, we determine the largest number of maximal independent sets among all connected graphs of order n, which contain at most one cycle. We also characterize those extremal graphs achieving this maximum value. As a consequence, the corresponding results for graphs with at most one cycle bu