Circuit or Closed Path A circuit is a path which starts and ends at the same vertex. A tree T is a graph that s both connected and acyclic. Zmazek, B. Zerovnik, Unique square property and fundamental factorizations of graph bundles , Discrete Math. For example trigonometry is used in developing computer music as you are familiar that sound travels in the form of waves and this wave pattern through a sine or cosine function for developing computer music. Find an article that describes how Graph theory is used and What are real world applications of graphs Graphs are Let 39 s move on to another application domain of graph theory biological networks.
Eternal dominating set
For example, let G be the double star graph consisting of vertices x 1 , The distinction between star-domination and usual domination is more substantial when their fractional variants are considered. Clearly, if G has isolated vertices then it has no star-dominating sets since the star of isolated vertices is empty. Namespaces Article Talk. The domination number of this graph is 2: the examples b and c show that there is a dominating set with 2 vertices, and it can be checked that there is no dominating set with only 1 vertex for this graph. The independent domination number i G of a graph G is the size of the smallest dominating set that is an independent set. In , Richard Karp proved the set cover problem to be NP-complete.
Eternal dominating set - Wikipedia
The edges of G are defined as follows: each x i is adjacent to a , a is adjacent to b , and b is adjacent to each b j. Therefore a minimum maximal matching has the same size as a minimum edge dominating set. There exist a pair of polynomial-time L-reductions between the minimum dominating set problem and the set cover problem. A minimum dominating set of an n -vertex graph can be found in time O 2 n n by inspecting all vertex subsets.
Description: This had immediate implications for the dominating set problem, as there are straightforward vertex to set and edge to non-disjoint-intersection bijections between the two problems. The independent domination number i G of a graph G is the size of the smallest dominating set that is an independent set. Equivalently, it is the size of the smallest maximal independent set. A dominating set may or may not be an independent set. A total dominating set is a set of vertices such that all vertices in the graph including the vertices in the dominating set themselves have a neighbor in the dominating set.