Q. The spectrum of a graph is _______ if and only if it is _______ graph.

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Q. In a 7-node directed cyclic graph, the number of Hamiltonian cycle is to be ______

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Q. If each and every vertex in G has degree at most 23 then G can have a vertex colouring of __________

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Q. Triangle free graphs have the property of clique number is __________

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Q. Berge graph is similar to ______ due to strong perfect graph theorem.

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Q. Let D be a simple graph on 10 vertices such that there is a vertex of degree 1, a vertex of degree 2, a vertex of degree 3, a vertex of degree 4, a vertex of degree 5, a vertex of degree 6, a vertex of degree 7, a vertex of degree 8 and a vertex of degree 9. What can be the degree of the last vertex?

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Q. A ______ is a graph which has the same number of edges as its complement must have number of vertices congruent to 4m or 4m modulo 4(for integral values of number of edges).

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Q. In a ______ the vertex set and the edge set are finite sets.

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Q. If G is the forest with 54 vertices and 17 connected components, G has _______ total number of edges.

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Q. The number of edges in a regular graph of degree 46 and 8 vertices is ____________

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Q. An undirected graph G has bit strings of length 100 in its vertices and there is an edge between vertex u and vertex v if and only if u and v differ in exactly one bit position. Determine the ratio of the chromatic number of G to the diameter of G?

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Q. A bridge can not be a part of _______

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Q. 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 _______

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Q. 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 ______

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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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