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Abstract
Let G = (V;E) be a simple graph. A set D\subset V is a dominating set of G if every vertex in V - D has at least one neighbor in D. The distance d_G(u, v) between two vertices u and v is the length of a shortest (u, v)-path in G. An (u, v)-path of length d_G(u; v) is called an (u, v)-geodesic. A set X\subset V is convex in G if vertices from all (a, b)-geodesics belong to X for any two vertices a, b \in X. A set X is a convex dominating set if it is convex and dominating set. The convex domination number \gamma_con(G) of a graph G equals the minimum cardinality of a convex dominating set in G. The convex domination subdivision number sd_con (G) is the minimum number of edges that must be subdivided (each edge in G can be subdivided at most once) in order to increase the convex domination number. In this paper we initiate the study of convex domination subdivision number and we establish upper bounds for it.
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Authors (4)
-
Saeed Kosary
- Azarbaijan Shahid Madani University Department of Mathematics
-
Seyed Sheikholeslami
- Azarbaijan Shahid Madani University Department of Mathematics
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Details
- Category:
- Articles
- Type:
- publikacja w in. zagranicznym czasopiśmie naukowym (tylko język obcy)
- Published in:
-
Communications in Combinatorics and Optimization
no. 1,
pages 43 - 56,
ISSN: 2538-2128 - Language:
- English
- Publication year:
- 2016
- Bibliographic description:
- Dettlaff M., Lemańska M., Kosary S., Sheikholeslami S.. The convex domination subdivision number of a graph. Communications in Combinatorics and Optimization, 2016, Vol. 1, nr. 1, s.43-56
- DOI:
- Digital Object Identifier (open in new tab) 10.22049/cco.2016.13544
- Verified by:
- Gdańsk University of Technology
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