32,834 research outputs found
On the algorithmic complexity of twelve covering and independence parameters of graphs
The definitions of four previously studied parameters related to total coverings and total matchings of graphs can be restricted, thereby obtaining eight parameters related to covering and independence, each of which has been studied previously in some form. Here we survey briefly results concerning total coverings and total matchings of graphs, and consider the aforementioned 12 covering and independence parameters with regard to algorithmic complexity. We survey briefly known results for several graph classes, and obtain new NP-completeness results for the minimum total cover and maximum minimal total cover problems in planar graphs, the minimum maximal total matching problem in bipartite and chordal graphs, and the minimum independent dominating set problem in planar cubic graphs
Gamma-Set Domination Graphs. I: Complete Biorientations of \u3cem\u3eq-\u3c/em\u3eExtended Stars and Wounded Spider Graphs
The domination number of a graph G, γ(G), and the domination graph of a digraph D, dom(D) are integrated in this paper. The γ-set domination graph of the complete biorientation of a graph G, domγ(G) is created. All γ-sets of specific trees T are found, and dom-γ(T) is characterized for those classes
On a Class of Graphs with Large Total Domination Number
Let and denote the domination number and the total
domination number, respectively, of a graph with no isolated vertices. It
is well-known that . We provide a characterization
of a large family of graphs (including chordal graphs) satisfying , strictly generalizing the results of Henning (2001) and Hou et al.
(2010), and partially answering an open question of Henning (2009).Comment: 9 pages, 4 figure
New results on metric-locating-dominating sets of graphs
A dominating set S of a graph is a metric-locating-dominating set if each vertex of the graph is uniquely distinguished by its distanc es from the elements of S , and the minimum cardinality of such a set is called the metri c-location- domination number. In this paper, we undertake a study that, in general graphs and specific families, relates metric-locating-dominatin g sets to other special sets: resolving sets, dominating sets, locating-dominating set s and doubly resolving sets. We first characterize classes of trees according to cer tain relationships between their metric-location-domination number and thei r metric dimension and domination number. Then, we show different methods to tran sform metric- locating-dominating sets into locating-dominating sets a nd doubly resolving sets. Our methods produce new bounds on the minimum cardinalities of all those sets, some of them involving parameters that have not been related so farPostprint (published version
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