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The second largest number of maximal independent sets in connected graphs with at most one cycle

✍ 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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Maximal independent sets in graphs with
✍ Min-Jen Jou; Gerard J. Chang πŸ“‚ Article πŸ“… 1997 πŸ› Elsevier Science 🌐 English βš– 356 KB

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

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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,

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## 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__ β‰₯ 3__r__. Β© 2006 Wiley Period

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✍ Bruce E. Sagan; Vincent R. Vatter πŸ“‚ Article πŸ“… 2006 πŸ› John Wiley and Sons 🌐 English βš– 236 KB πŸ‘ 2 views

## 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

The number of maximal independent sets i
✍ Jerrold R. Griggs; Charles M. Grinstead; David R. Guichard πŸ“‚ Article πŸ“… 1988 πŸ› Elsevier Science 🌐 English βš– 1021 KB

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