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21. T is a graph with n vertices. T is connected and has exactly n-1 edges, then
T is a tree
T contains no cycles
every pair of vertices in T is connected by exactly one path
addition of a new edge will create a cycle
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22. The length of a Hamiltanian path (if exists) in a connected graph of n vertices is
n-1
n
n+1
n/2
23. A simple graph in which there exists an edge between every pair of vertices is called
complete graph
eular graph
planner graph
regular graph
24. The minimum number of spanning trees in a connected graph with 'n' nodes is
1
2
n - 1
25. If a graph requires k different colours for its proper colouring, then chromatic number of the graph is
k
k-1
k/2
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