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Abstract
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 αc(G), as the greatest integer r such that every vertex of G belongs to some independent subset X of VG with |X| ≥ r. The common independence number αc(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 αc(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) ≤ αc(G) ≤ α(G). In this paper, we characterize the trees T for which i(T) = αc(T), and the block graphs G for which αc(G) = α(G).
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Authors (3)
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Jerzy Topp
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- Publication version
- Accepted or Published Version
- DOI:
- Digital Object Identifier (open in new tab) 10.3390/sym13081411
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- Category:
- Articles
- Type:
- artykuły w czasopismach
- Published in:
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Symmetry-Basel
no. 13,
ISSN: 2073-8994 - Language:
- English
- Publication year:
- 2021
- Bibliographic description:
- Lemańska M., Dettlaff M., Topp J.: Common Independence in Graphs// Symmetry-Basel -,iss. 13 (2021),
- DOI:
- Digital Object Identifier (open in new tab) 10.3390/sym13081411
- Verified by:
- Gdańsk University of Technology
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