• Corpus ID: 973043

Counting non-isomorphic maximal independent sets of the n-cycle graph

@article{Bisdorff2007CountingNM,
  title={Counting non-isomorphic maximal independent sets of the n-cycle graph},
  author={Raymond Bisdorff and Jean-Luc Marichal},
  journal={ArXiv},
  year={2007},
  volume={abs/math/0701647}
}
The number of maximal independent sets of the n-cycle graph Cn is known to be the nth term of the Perrin sequence. The action of the automorphism group of Cn on the family of these maximal independent sets partitions this family into disjoint orbits, which represent the non-isomorphic (i.e., defined up to a rotation and a reflection) maximal independent sets. We provide exact formulas for the total number of orbits and the number of orbits having a given number of isomorphic representatives. We… 

Figures and Tables from this paper

Maximal independent sets in grid graphs
TLDR
This work provides a polynomial-time algorithm to generate the whole family of maximal independent sets (mis) of complete grid graphs with two rows and applies this result to characterize the independent graph (intersection graph of maximalindependent sets) of these three classes of graphs.
Maximal Independent Sets in Polygonal Cacti
Counting the number of maximal independent sets of graphs was started over 50 years ago by Erd˝os and Mooser. The problem has been continuously studied with a number of variations. Interestingly,
MAXIMAL INDEPENDENT SET BASED APPROACH FOR GRAPH COLORING PROBLEM
TLDR
This work proposes an approach which solves the graph coloring problem more efficiently by providing minimum number of colors with effectively lesser time than that of the fastest exact algorithm till date.
Counting Hidden Neural Networks
We apply combinatorial tools, including Pólya’s theorem, to enumerate all possible networks for which (1) the network contains distinguishable input and output nodes as well as partially
Fused Fibonacci-like (p,q) sequences with compression and barcoding applications
TLDR
A new concept of generating parametric number representations by fusing systems such as DBNS using multiplication and addition operations is presented and Fibonacci like (p,q)-sequences are introduced and their efficiency in representing data is determined.
An energy-efficient adaptive clustering algorithm with load balancing for wireless sensor network
TLDR
A Density-based Dynamic Clustering algorithm for clustering and cluster head election mechanism with the use of independence set is proposed, and a distributed algorithm (DISD - Distributed Independence Set Discovery) is designed for cluster headelection in O(1) complexity per sensor node.

References

SHOWING 1-10 OF 18 REFERENCES
The Fibonacci Number of a Grid Graph and a New Class of Integer Sequences
Given a grid graph G of size mn, we study the number i(m; n) of independent sets in G, as well as b(m; n), the number of maximal such sets. It turns out that the initial cases b(1; n) and b(2; n)
Maximal independent sets in graphs with at most r cycles
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
The number of maximal independent sets in connected graphs
TLDR
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.
Algebraic Graph Theory
TLDR
The Laplacian of a Graph and Cuts and Flows are compared to the Rank Polynomial.
The On-Line Encyclopedia of Integer Sequences
  • N. Sloane
  • Computer Science
    Electron. J. Comb.
  • 1994
TLDR
The On-Line Encyclopedia of Integer Sequences (or OEIS) is a database of some 130000 number sequences which serves as a dictionary, to tell the user what is known about a particular sequence and is widely used.
Independent sets on path-schemes
We give the generating function for the number of independent sets on the class of well-based path-schemes (a kind of regularly structured graph), which generalizes the known result in this direction.
Alice through Looking Glass after Looking Glass: The Mathematics of Mirrors and Kaleidoscopes
TLDR
Coxeter’s results are described, emphasizing the connection with kaleidoscopes, and some linear algebra (including determinants), basic group theory, and a bit of graph theory are involved.
Mathematics Subject Classification: Primary 05C69; Secondary 05C38
  • Mathematics Subject Classification: Primary 05C69; Secondary 05C38
  • 1155
...
...