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On the number of independent sets in damaged Cayley graphs.
- Source :
-
Discrete Mathematics & Applications . 2005, Vol. 15 Issue 4, p361-364. 4p. - Publication Year :
- 2005
-
Abstract
- The Cayley graph generated by a set A is the graph ΓA(V) on a set of positive integers V such that a pair(u,v) ∈ V×V is an edge of the graph if and only if |u-v| ∈ A or u+v ∈ A. We denote by G2(n,m) the class of graphs G = (V, E) such that G is a union of chains and cycles and |V| = n, |E| = m. In this paper, we present an upper bound for the number of independent sets in Cayley graphs ΓA(V) such that A = {⌈n/2⌉ - t, ⌈n/2⌉ - ƒ}, V &subE; [⌊n/2⌋ + 1, ⌊n/2⌋+t] ∪ [n - t + 1, n], where n, t, ƒ ∈ N and ƒ < t < n/4. We also describe the graph with the maximum number of independent sets in the family g2(n, m). This research was supported by the Russian Foundation for Basic Researches, grant 04–01–00359. [ABSTRACT FROM AUTHOR]
- Subjects :
- *CAYLEY graphs
*SET theory
*GRAPH theory
*ALGEBRA
*MATHEMATICS
Subjects
Details
- Language :
- English
- ISSN :
- 09249265
- Volume :
- 15
- Issue :
- 4
- Database :
- Academic Search Index
- Journal :
- Discrete Mathematics & Applications
- Publication Type :
- Academic Journal
- Accession number :
- 18535479
- Full Text :
- https://doi.org/10.1515/156939205774464954