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Weakly convex domination subdivision number of a graph

Abstract

A set X is weakly convex in G if for any two vertices a; b \in X there exists an ab–geodesic such that all of its vertices belong to X. A set X \subset V is a weakly convex dominating set if X is weakly convex and dominating. The weakly convex domination number \gamma_wcon(G) of a graph G equals the minimum cardinality of a weakly convex dominating set in G. The weakly convex domination subdivision number sd_wcon (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 weakly convex domination number. In this paper we initiate the study of weakly convex domination subdivision number and establish upper bounds for it.

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Category:
Articles
Type:
artykuł w czasopiśmie wyróżnionym w JCR
Published in:
FILOMAT no. 30, edition 8, pages 2101 - 2110,
ISSN: 0354-5180
Language:
English
Publication year:
2016
Bibliographic description:
Dettlaff M., Kosary S., Lemańska M., Sheikholeslami S.: Weakly convex domination subdivision number of a graph// FILOMAT. -Vol. 30, iss. 8 (2016), s.2101-2110
DOI:
Digital Object Identifier (open in new tab) 10.2298/fil1608101d
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