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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Q. A walk has Closed property if ____________

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Q. A trail in a graph can be described as ______________

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Q. Let a graph can be denoted as ncfkedn a kind of ____________

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Q. Determine the edge count of a path complement graph with 14 vertices.

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Q. The sum of an n-node graph and its complement graph produces a graph called _______

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Q. 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?

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Q. 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)?

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