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Similarities and Differences Between the Vertex Cover Number and the Weakly Connected Domination Number of a Graph
Abstract
A vertex cover of a graph G = (V, E) is a set X ⊂ V such that each edge of G is incident to at least one vertex of X. The ve cardinality of a vertex cover of G. A dominating set D ⊆ V is a weakly connected dominating set of G if the subgraph G[D]w = (N[D], Ew) weakly induced by D, is connected, where Ew is the set of all edges having at least one vertex in D. The weakly connected domination number γw(G) of G is the minimum cardinality among all weakly connected dominating sets of G. In this article we characterize the graphs where γw(G) = τ (G). In particular, we focus our attention on bipartite graphs, regular graphs, unicyclic graphs, block graphs and corona graphs.
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Authors (3)
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Juan A. RODRíGUEZ-VELáZQUEZ
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Rolando Trujillo-Rasua
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Details
- Category:
- Articles
- Type:
- artykuł w czasopiśmie wyróżnionym w JCR
- Published in:
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FUNDAMENTA INFORMATICAE
no. 152,
edition 3,
pages 273 - 287,
ISSN: 0169-2968 - Language:
- English
- Publication year:
- 2017
- Bibliographic description:
- Lemańska M., Rodríguez-Velázquez J., Trujillo-Rasua R.: Similarities and Differences Between the Vertex Cover Number and the Weakly Connected Domination Number of a Graph// FUNDAMENTA INFORMATICAE. -Vol. 152, iss. 3 (2017), s.273-287
- DOI:
- Digital Object Identifier (open in new tab) 10.3233/fi-2017-1520
- Verified by:
- Gdańsk University of Technology
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