The number of maximal independent sets in a connected graph
Reads0
Chats0
TLDR
The maximum number of maximal independent sets which a connected graph on n vertices can have is determined, and the extremal graphs are completely characterize, thereby answering a question of Wilf.About:
This article is published in Discrete Mathematics.The article was published on 1988-02-01 and is currently open access. It has received 92 citations till now. The article focuses on the topics: Maximal independent set & Independent set.read more
Citations
More filters
Maximal Independent Sets in Polygonal Cacti
Natawat Klamsakul,Pantaree Thengarnanchai,Mattanaporn Suebtangjai,Pailin Kaewperm,Nuttanon Songsuwan,Pawaton Kaemawichanurat +5 more
TL;DR: In this article , the authors applied the concept of bivariate generating function to establish the recurrence relations of the number of maximal independent sets of regualr n -gonal cacti when 3 ≤ n ≤ 6.
Journal ArticleDOI
Multi-Hop Task Routing in UAV-Assisted Mobile Edge Computing IoT Networks with Intelligent Reflective Surfaces
TL;DR: In this paper , the authors proposed a multi-hop task routing solution for Internet of Things (IoT) networks in which a UAV can also relay to another UAV with better connection to a ground MEC server.
Journal ArticleDOI
Counting maximal independent sets in some <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e4136" altimg="si77.svg"><mml:mi>n</mml:mi></mml:math>-gonal cacti
Natawat Klamsakul,Pantaree Thengarnanchai,Mattanaporn Suebtangjai,Pailin Kaewperm,Nuttanon Songsuwan,Pawaton Kaemawichanurat +5 more
TL;DR: In this paper , the authors applied the concept of bivariate generating function to establish the recurrence relations of the number of maximal independent sets of regular n-gonal cacti when 3≤n≤6.
Journal ArticleDOI
The second largest number of maximal independent sets in graphs with at most two cycles
Min-Jen Jou,Jenq-Jong Lin +1 more
TL;DR: In this article, the second largest number of maximal independent sets among all graphs of order n ≥ 5 with at most two cycles was shown. But the maximal independent set is an independent set that is not a proper subset of any other independent set.
DissertationDOI
Some counting problems in graphs
TL;DR: In this paper, the authors give upper and lower bounds on the number of subsets of the vertex set of a graph with certain properties, often they also characterize the extremal graphs.
References
More filters
Journal ArticleDOI
On cliques in graphs
J. W. Moon,L. Moser +1 more
TL;DR: In this article, the maximum number of cliques possible in a graph with n nodes is determined and bounds are obtained for the number of different sizes of clique possible in such a graph.
Journal ArticleDOI
The number of maximal independent sets in a tree
TL;DR: In this paper, the maximal independent sets of vertices that any tree of n vertices can have were shown to have maximal number of maximal independent vertices, where vertices are independent sets.
Journal ArticleDOI
The number of maximal independent sets in connected graphs
TL;DR: A theorem of Moon and Moser is generalized to determine the maximum number of maximal independent sets in a connected graph on n vertices for n sufficiently large, e.g., n > 50.