## 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
Maximal independent sets in caterpillar graphs
✍ Scribed by Carmen Ortiz; Mónica Villanueva
- Book ID
- 113564715
- Publisher
- Elsevier Science
- Year
- 2012
- Tongue
- English
- Weight
- 520 KB
- Volume
- 160
- Category
- Article
- ISSN
- 0166-218X
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📜 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,
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
## 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. Erdös, 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__ ≥ 3__r__. © 2006 Wiley Period