Which of the following techniques algorithms can be used to find number of connected components in an undirected graph with V vertices and E edges?
We can use a traversal algorithm, either depth-first or breadth-first, to find the connected components of an undirected graph. If we do a traversal starting from a vertex v, then we will visit all the vertices that can be reached from v. These are the vertices in the connected component that contains v.
How can we use BFS to determine if an undirected graph is connected that is there is a path between any two vertices?
Approach: Either Breadth First Search (BFS) or Depth First Search (DFS) can be used to find path between two vertices. Take the first vertex as source in BFS (or DFS), follow the standard BFS (or DFS). If the second vertex is found in our traversal, then return true else return false.
What is the formula you would use to find the number of edges in a complete graph with n vertices?
The maximum number of edges possible in a single graph with ‘n’ vertices is nC2 where nC2 = n(n – 1)/2.
How do you find the number of undirected graphs?
4 Answers. Graph with N vertices may have up to C(N,2) = (N choose 2) = N*(N-1)/2 edges (if loops aren’t allowed). So overall number of possible graphs is 2^(N*(N-1)/2) .
How many total number of edges present in complete undirected graph if it has n nodes?
A complete graph is a graph in which every pair of vertices is connected by exactly one edge. So a complete graph on n vertices contains n(n – 1)/2 edges and your question is equivalent to asking what value of n makes n(n – 1)/2 = 45. 10 x 9/2 = 45 so the answer is 10.
Do undirected graphs have cycles?
An undirected graph is acyclic (i.e., a forest) if a DFS yields no back edges. Since back edges are those edges ( u , v ) connecting a vertex u to an ancestor v in a depth-first tree, so no back edges means there are only tree edges, so there is no cycle.
How to find the set of paths in a graph G-T?
Moreover, there is a one to one correspondence between the set of paths P 1 and the set of s – t ′ paths in the graph G − t. Thus, we get an easy recursive algorithm to find the set of paths s – t paths in a graph G. Pick an edge t t ′ incident the vertex t and recursively calculate the sets P 1 and P 2.
Can an undirected graph be transformed to a directed graph?
The reason is that any undirected graph can be transformed to its equivalent directed graph by replacing each undirected edge with two directed edges and . However, in undirected graphs, there’s a special case where the graph forms a tree. We’ll discuss this case separately. 5. Trees
How many times can a vertex appear in a simple path?
For each two consecutive vertices , where , there is an edge that belongs to the set of edges There is no vertex that appears more than once in the sequence; in other words, the simple path has no cycles
How many simple paths are there in a graph?
For example, let’s consider the graph: As we can see, there are 5 simple paths between vertices 1 and 4: Note that the path is not simple because it contains a cycle — vertex 4 appears two times in the sequence. 3. Algorithm 3.1.