INDEPENDANT DOMINATION GRAPH THEORY


Independant Domination Graph Theory

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Independent domination in regular graphs - ScienceDirect

They also discuss aproximating algortihms for some other types of graphs.

  • Questions Tags Users Badges Unanswered. Algorithm for the independent domination number.
  • From dominating set to set covering. I is a clique and U is an independent set.
  • The subsets S 2 , S 3 , and S 4 are the independent vertex sets because there is no vertex that is adjacent to any one vertex from the subsets. In S 1 and S 4 , we can add other vertices; but in S 2 and S 3 , we cannot add any other vertex.
  • The subsets S 2 , S 3 , and S 4 are the independent vertex sets because there is no vertex that is adjacent to any one vertex from the subsets.

They have also been used in document summarization, and in designing secure systems for electrical grids. The subsets S 2 , S 3 , and S 4 are the independent vertex sets because there is no vertex that is adjacent to any one vertex from the subsets. In this example, the subsets L 2 and L 3 are clearly not the adjacent edges in the given graph. In , Richard Karp proved the set cover problem to be NP-complete. Nate River 2, 1 5

DESCRIPTION: Both problems are in fact Log-APX-complete. Sign up or log in Sign up using Google. An independent set in L G corresponds to a matching in G , and a dominating set in L G corresponds to an edge dominating set in G.


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Therefore a minimum maximal matching has the same size as a minimum edge dominating set. Views Read Edit View history. On the other hand, if the input graph is planar, the problem remains NP-hard, but a fixed-parameter algorithm is known. By clicking "Post Your Answer", you acknowledge that you have read our updated terms of service , privacy policy and cookie policy , and that your continued use of the website is subject to these policies. In , Richard Karp proved the set cover problem to be NP-complete. In each example, each white vertex is adjacent to at least one red vertex, and it is said that the white vertex is dominated by the red vertex. This site uses cookies to deliver our services and to show you relevant ads and job listings.

Dominating set

Here they show a random polynomial time approximation algorithm for this problem in some special graphs. Dominating sets are of practical interest in several areas. A minimum dominating set of an n -vertex graph can be found in time O 2 n n by inspecting all vertex subsets. Hence these two subsets are considered as the maximal independent line sets.

  • Graph Theory - Independent Sets
  • On the other hand, if the input graph is planar, the problem remains NP-hard, but a fixed-parameter algorithm is known.
  • Maximal Independent Line Set
  • Figures a — c on the right show three examples of dominating sets for a graph.

Clearly S 1 is not an independent vertex set, because for getting an independent vertex set, there should be at least two vertices in the from a graph. The number of minimal dominating sets is at most 1. Algorithm for the independent domination number. The domatic number is the maximum size of a domatic partition.

Independent Line Set

Post as a guest Name. This page was last edited on 16 May , at Vizing's conjecture relates the domination number of a cartesian product of graphs to the domination number of its factors. The set cover problem is a well-known NP-hard problem — the decision version of set covering was one of Karp's 21 NP-complete problems. In , Richard Karp proved the set cover problem to be NP-complete.

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