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
The second largest number of maximal independent sets in connected graphs with at most one cycle
β Scribed by Min-Jen Jou
- Book ID
- 118801970
- Publisher
- Springer US
- Year
- 2011
- Tongue
- English
- Weight
- 420 KB
- Volume
- 24
- Category
- Article
- ISSN
- 1382-6905
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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 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
## Abstract Let __m__(__G__) denote the number of maximal independent sets of vertices in a graph __G__ and let __c__(__n__,__r__) be the maximum value of __m__(__G__) over all connected graphs with __n__ vertices and at most __r__ cycles. A theorem of Griggs, Grinstead, and Guichard gives a formul
We determine the maximum on n vertices can have, and we a question of Wilf. number of maximal independent sets which a connected graph completely characterize the extremal graphs, thereby answering \* Partially supported by NSF grant number DIMS-8401281. t Partially supported by NSF grant number D S