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Common Independence in Graphs.
- Source :
-
Symmetry (20738994) . Aug2021, Vol. 13 Issue 8, p1411. 1p. - Publication Year :
- 2021
-
Abstract
- The cardinality of a largest independent set of G, denoted by α (G) , is called the independence number of G. The independent domination number i (G) of a graph G is the cardinality of a smallest independent dominating set of G. We introduce the concept of the common independence number of a graph G, denoted by α c (G) , as the greatest integer r such that every vertex of G belongs to some independent subset X of V G with | X | ≥ r . The common independence number α c (G) of G is the limit of symmetry in G with respect to the fact that each vertex of G belongs to an independent set of cardinality α c (G) in G, and there are vertices in G that do not belong to any larger independent set in G. For any graph G, the relations between above parameters are given by the chain of inequalities i (G) ≤ α c (G) ≤ α (G) . In this paper, we characterize the trees T for which i (T) = α c (T) , and the block graphs G for which α c (G) = α (G) . [ABSTRACT FROM AUTHOR]
- Subjects :
- *DOMINATING set
*INDEPENDENT sets
*INTEGERS
Subjects
Details
- Language :
- English
- ISSN :
- 20738994
- Volume :
- 13
- Issue :
- 8
- Database :
- Academic Search Index
- Journal :
- Symmetry (20738994)
- Publication Type :
- Academic Journal
- Accession number :
- 152127639
- Full Text :
- https://doi.org/10.3390/sym13081411