Q. 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.

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Q. 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?

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Q. ______ is the maximum number of edges in an acyclic undirected graph with k vertices.

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Q. The minimum number of edges in a connected cyclic graph on n vertices is _____________

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Q. The maximum number of edges in a 8-node undirected graph without self loops is ____________

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Q. 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 _____

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Q. The 2ⁿ vertices of a graph G corresponds to all subsets of a set of size n, for n>=4. Two vertices of G are adjacent if and only if the corresponding sets intersect in exactly two elements.
The number of connected components in G can be ___________

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Q. 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).

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Q. Every Isomorphic graph must have ________ representation.

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Q. A cycle on n vertices is isomorphic to its complement. What is the value of n?

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Q. How many perfect matchings are there in a complete graph of 10 vertices?

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Q. 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)

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Q. A complete n-node graph Kn is planar if and only if _____________

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Q. A graph is ______ if and only if it does not contain a subgraph homeomorphic to k₅ or k₃,₃.

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Q. An isomorphism of graphs G and H is a bijection f the vertex sets of G and H. Such that any two vertices u and v of G are adjacent in G if and only if ____________

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Q. What is the grade of a planar graph consisting of 8 vertices and 15 edges?

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Q. A _______ is a graph with no homomorphism to any proper subgraph.

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Q. Which algorithm efficiently calculates the single source shortest paths in a Directed Acyclic Graph?

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Q. The _______ of a graph G consists of all vertices and edges of G.

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Q. A ______ in a graph G is a circuit which consists of every vertex (except first/last vertex) of G exactly once.

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