3. binary tree
A bridge can not be a part of _______
1.a simple cycle
3.a clique with size ≥ 3 whose every edge is a bridge
4.a graph which contains cycles
A graph G has the degree of each vertex is ≥ 3 say, deg(V) ≥ 3 ∀ V ∈ G such that 3|V| ≤ 2|E| and 3|R| ≤ 2|E|, then the graph is said to be ________ (R denotes region in the graph)
A graph which has the same number of edges as its complement must have number of vertices congruent to ______ or _______ modulo 4(for integral values of number of edges).
4. 2k+1, k
3.either true or false
A polytree is called _______________
1.directed acyclic graph
2.directed cyclic graph
1.a walk without repeated edges
2.a cycle with repeated edges
3.a walk with repeated edges
4.a line graph with one or more vertices
A ______ in a graph G is a circuit which consists of every vertex (except first/last vertex) of G exactly once.
4.Path complement graph
Any subset of edges that connects all the vertices and has minimum total weight, if all the edge weights of an undirected graph are positive is called _______
G is a simple undirected graph and some vertices of G are of odd degree. Add a node n to G and make it adjacent to each odd degree vertex of G. The resultant graph is ______
1.Complete bipartite graph
If G is a simple graph with n-vertices and n>=3, the condition for G has a Hamiltonian circuit is __________
1.the degree of each vertex is at most n/2
2.the degree of each vertex is equal to n
3.the degree of every vertex is at least n+1/2
4.the degree of every vertex in G is at least n/2
If there are more than 1 topological sorting of a DAG is possible, which of the following is true.
1.Many Hamiltonian paths are possible
2.No Hamiltonian path is possible
3.Exactly 1 Hamiltonian path is possible
4.Given information is insufficient to comment anything
If two cycle graphs Gm and Gn are joined together with a vertex, the number of spanning trees in the new graph is ______
In a directed weighted graph, if the weight of every edge is decreased by 10 units, does any change occur to the shortest path in the modified graph?
1.Representation of Boolean Functions
4.Sorting of number
3.Manipulations on numbers
2. line graph
Let G be a directed graph whose vertex set is the set of numbers from 1 to 50. There is an edge from a vertex i to a vertex j if and only if either j = i + 1 or j = 3i. Calculate the minimum number of edges in a path in G from vertex 1 to vertex 50.
Let G be an arbitrary graph with v nodes and k components. If a vertex is removed from G, the number of components in the resultant graph must necessarily lie down between _____ and _____
1.n-1 and n+1
2.v and k
3.k+1 and v-k
4.k-1 and v-1
Let G(V, E) be a directed graph where every edge has weight as either 1, 2 or 5, what is the algorithm used for the shortest path from a given source vertex to a given destination vertex to get the time complexity of O(V+E)?
The maximum number of edges in a 8-node undirected graph without self loops is ____________
1.n – 1
The tree elements are called __________
3.path complement graph
1.graphs of the two trees are isomorphic
2.the two trees have same label
3.graphs of the two trees are isomorphic and the two trees have the same label
4.graphs of the two trees are cyclic
What is a bipartite graph?
1.a graph which contains only one cycle
2.a graph which consists of more than 3 number of vertices
3.a graph which has odd number of vertices and even number of edges
4.a graph which contains no cycles of odd length
What is a separable graph?
1.A disconnected graph by deleting a vertex
2.A disconnected graph by removing an edge
3.A disconnected graph by removing one edge and a vertex
4.A simple graph which does not contain a cycle
What is a star tree?
1.A tree having a single internal vertex and n-1 leaves
2.A tree having n vertices arranged in a line
3.A tree which has 0 or more connected subtrees
4.A tree which contains n vertices and n-1 cycles
What is the number of vertices in an undirected connected graph with 39 edges, 7 vertices of degree 2, 2 vertices of degree 5 and remaining of degree 6?
What is the value of the sum of the minimum in-degree and maximum out-degree of an Directed Acyclic Graph?
1.Depends on a Graph
2.Will always be zero
3.Will always be greater than zero
4.May be zero or greater than zero
What is time complexity to check if a string(length S1) is a substring of another string(length S2) stored in a Directed Acyclic Word Graph, given S2 is greater than S1?
Which algorithm efficiently calculates the single source shortest paths in a Directed Acyclic Graph?
Which of the given statement is true?
1.All the Cyclic Directed Graphs have topological sortings
2.All the Acyclic Directed Graphs have topological sortings
3.All Directed Graphs have topological sortings
4.All the cyclic directed graphs hace non topological sortings