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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?
The line graph L(G) of a simple graph G is defined as follows: There is exactly one vertex v(e) in L(G) for each edge e in G. For any two edges e and e' in G, L(G) has an edge between v(e) and v(e'), if and only if e and e' are incident with the same vertex in G. Which of the following statements is/are TRUE? (P) The line graph of a cycle is a cycle. (Q) The line graph of a clique is a clique. (R) The line graph of a planar graph is planar. (S) The line graph of a tree is a tree.
Let G be a directed graph whose vertex set is the set of numbers from 1 to 100. There is an edge from a vertex i to a vertex j if and only if either j = i + 1 or j = 3i. The minimum number of edges in a path in G from vertex 1 to vertex 100 is 
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.
Garima starts walking towards the south from point R. He walks for 5m to reach Point S then turns right and walks for 2m to reach point T from there he turns left and walks for 3m to reach Point Z. He then turns right from point Z and walks for 6m to reach point Y and then turns right and walks for 3m to reach point X. He then turns right from point X and walks for 4m to reach point W and then turns left and walks for 5m to reach point V and then turns left and walks for 4m till point U and stops. What is the shortest distance between point V and point R?
A person wants to visit some places. He starts from a vertex and then wants to visit every vertex till it finishes from one vertex, backtracks and then explore other vertex from same vertex. What algorithm he should use?
In the given graph, identify the shortest path having minimum cost to reach vertex E if A is the source vertex.
Availability of drinking water is continuously decreasing. The government decided to identify those sources of drinking water which getting polluted. The following table depicts the number of polluted sources in a district. Source of drinking water getting polluted Number Wells 24 Handpump 12 Dam 12 Borewell 6 Ponds 18 The pictograph table for the above table will be (A) Source of drinking water getting polluted Number symbol = 6 source Wells Handpump Dam Borewell Ponds (B) Source of drinking water getting polluted Number symbol  = 6 source Wells Handpump Dam Borewell Ponds (C) Source of drinking water getting polluted Number symbol  = 6 source Wells Handpump Dam Borewell Ponds (D) Source of drinking water getting polluted Number symbol  = 6 source Wells Handpump Dam Borewell Ponds
A man starts from point ‘O’, travels 20 km towards east to reach point ‘A’, turns right and travels 10 km to reach point ‘B', turns right and travels 9 km to reach point ‘C’, turns right and travels 5 km to reach point ‘D’, turns left and travels 12 km to reach point ‘E’ and then turns right and travels 6 km to reach point ‘F. What is the shortest distance between point ‘E’ and point ‘C’?
A man starts from point 'O', travels 20 km towards east to reach point 'A', turns right and travels 10 km to reach point 'B', turns right and travels 9 km to reach point 'C', turns right and travels 5 km to reach point 'D', turns left and travels 12 km to reach point 'E' and then turns right and travels 6 km to reach point 'F'. What is the shortest distance between point 'E' and point 'C'?