Nordhaus-Gaddum results for weakly convex domination number of a graph

2010 ◽  
Vol 30 (2) ◽  
pp. 257 ◽  
Author(s):  
Magdalena Lemańska
Keyword(s):  
Domination Number ◽  
Weakly Convex ◽  
Convex Domination Number

scholarly journals Weakly convex domination subdivision number of a graph

Filomat ◽  
2016 ◽  
Vol 30 (8) ◽  
pp. 2101-2110
Author(s):  
Magda Dettlaff ◽  
Saeed Kosary ◽  
Magdalena Lemańska ◽  
Seyed Sheikholeslami
Keyword(s):  
Dominating Set ◽  
Domination Number ◽  
Upper Bounds ◽  
Weakly Convex ◽  
Minimum Cardinality ◽  
Minimum Number ◽  
Convex Domination Number ◽  
Domination Subdivision Number

A set X is weakly convex in G if for any two vertices a,b ? X there exists an ab-geodesic such that all of its vertices belong to X. A set X ? V is a weakly convex dominating set if X is weakly convex and dominating. The weakly convex domination number ?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.

Nordhaus-Gaddum results for the convex domination number of a graph

2012 ◽  
Vol 65 (1) ◽  
pp. 125-134 ◽  
Author(s):  
M. Lemańska ◽  
J. A. Rodríguez-Velázquez ◽  
I. Gonzalez Yero
Keyword(s):  
Domination Number ◽  
Convex Domination Number

scholarly journals Convex dominating-geodetic partitions in graphs

Filomat ◽  
2016 ◽  
Vol 30 (11) ◽  
pp. 3075-3082
Author(s):  
Yero González ◽  
Magdalena Lemńska
Keyword(s):  
Present Article ◽  
Connected Graph ◽  
Dominating Set ◽  
Domination Number ◽  
Minimum Cardinality ◽  
Geodetic Number ◽  
Geodetic Set ◽  
Convex Domination Number

The distance d(u,v) between two vertices u and v in a connected graph G is the length of a shortest u-v path in G. A u-v path of length d(u,v) is called u-v geodesic. A set X is convex in G if vertices from all a -b geodesics belong to X for every two vertices a,b?X. A set of vertices D is dominating in G if every vertex of V-D has at least one neighbor in D. The convex domination number con(G) of a graph G equals the minimum cardinality of a convex dominating set in G. A set of vertices S of a graph G is a geodetic set of G if every vertex v ? S lies on a x-y geodesic between two vertices x,y of S. The minimum cardinality of a geodetic set of G is the geodetic number of G and it is denoted by g(G). Let D,S be a convex dominating set and a geodetic set in G, respectively. The two sets D and S form a convex dominating-geodetic partition of G if |D| + |S| = |V(G)|. Moreover, a convex dominating-geodetic partition of G is called optimal if D is a ?con(G)-set and S is a g(G)-set. In the present article we study the (optimal) convex dominating-geodetic partitions of graphs.

Graphs with convex domination number close to their order

2006 ◽  
Vol 26 (2) ◽  
pp. 307 ◽  
Author(s):  
Joanna Cyman ◽  
Magdalena Lemańska ◽  
Joanna Raczek
Keyword(s):  
Domination Number ◽  
Convex Domination Number

Outer-convex domination in graphs

2019 ◽  
Vol 12 (01) ◽  
pp. 2050008 ◽  
Author(s):  
Jonecis A. Dayap ◽  
Enrico L. Enriquez
Keyword(s):  
Convex Set ◽  
Dominating Set ◽  
Domination Number ◽  
Simple Graph ◽  
Dominating Sets ◽  
Minimum Cardinality ◽  
Convex Domination Number ◽  
Domination In Graphs

Let [Formula: see text] be a connected simple graph. A set [Formula: see text] of vertices of a graph [Formula: see text] is an outer-convex dominating set if every vertex not in [Formula: see text] is adjacent to some vertex in [Formula: see text] and [Formula: see text] is a convex set. The outer-convex domination number of [Formula: see text], denoted by [Formula: see text], is the minimum cardinality of an outer-convex dominating set of [Formula: see text]. An outer-convex dominating set of cardinality [Formula: see text] will be called a [Formula: see text]-[Formula: see text]. In this paper, we initiate the study and characterize the outer-convex dominating sets in the join of the two graphs.

Medium Domination Number of Certain Graphs

2018 ◽  
Vol 6 (11) ◽  
pp. 130
Author(s):  
K. Uma Samundesvari ◽  
J. Maria Regila Baby
Keyword(s):  
Domination Number

In this paper the author have found out the medium domination number of Helm graph, Friendship graph.

Strong Domination Number of some Path Related Graphs

2017 ◽  
Vol 7 (1) ◽  
pp. 109
Author(s):  
S. K. Vaidya ◽  
Sejal Hiteshbhai Karkar
Keyword(s):  
Domination Number
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