An independent set is a subset of vertices in undirected graph G such that no two are
connected by an edge.
A k-clique of a graph G is a subgraph of k vertices such that every pair is connected by
edges.
A cut in a graph is a partition of the vertices into two parts A and B. The size of the cut is
the number of edges with one end in A and the other in B.
A dominating set in a directed graph is a subset of vertices such that every vertex is either
in the subset or adjacent to at least one vertex in the subset.
A vertex cover in an undirected graph is a set of vertices such that every edge in the
graph is adjacent to some vertex in the set.
A path in a graph G is a finite sequence of edges in which any two consecutive edges are
adjacent, the first edge should begin with the vertex s and the last edge should end with
the vertex t. The cost of a path is the sum of the cost of its edges
A Hamilton Cycle in a graph is a finite sequence of edges in which any two consecutive
edges are adjacent such that by walking through the edges we visit every vertex exactly
once and return to the starting vertex.
A Traveling Salesperson problem is finding a finite sequence of edges in which any two
consecutive edges are adjacent such that by walking through the edges we visit every
vertex and return to the starting vertex.
An edge cover is a subset of edges such that all vertices are covered by these edges.
K-Coloring -The assignment of k colors to the vertices such that no two adjacent vertices
have the same color.