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Abstract
If $G=(V,E)$ is a simple connected graph and $a,b\in V$, then a shortest $(a-b)$ path is called a $(u-v)$-{\it geodesic}. A set $X\subseteq V$ is called {\it weakly convex} in $G$ if for every two vertices $a,b\in X$ exists $(a-b)$- geodesic whose all vertices belong to $X$. A set $X$ is {\it convex} in $G$ if for every $a,b\in X$ all vertices from every $(a-b)$-geodesic belong to $X$. The {\it weakly convex domination number} of a graph $G$ is the minimum cardinality of a weakly convex dominating set in $G$, while the {\it convex domination number} of a graph $G$ is the minimum cardinality of a convex dominating set in $G$. In this paper we consider weakly convex and convex domination numbers of Cartesian product, join and corona of some classes of graphs.
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- Category:
- Articles
- Type:
- artykuł w czasopiśmie wyróżnionym w JCR
- Published in:
-
ARS COMBINATORIA
no. 124,
pages 409 - 420,
ISSN: 0381-7032 - Language:
- English
- Publication year:
- 2016
- Bibliographic description:
- Kucieńska A., Lemańska M., Raczek J.: Weakly convex and convex domination numbers of some products of graphs// ARS COMBINATORIA. -Vol. 124, nr. 1 (2016), s.409-420
- Verified by:
- Gdańsk University of Technology
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