sir, in question number 8. they are asking maximum number of spanning trees.
they are saying answer is 3.
but if we take a cycle with 4 or 5 vertices and to make a spanning tree , we excluded one edge every time and we can make N such trees. how it is possible ?
plz share the complete question
sir, question is >>>Q8. MST What is the largest integer m such that every simple connected graph with n vertices and n edges contains at least m different spanning trees? options -> 1 , 2 , n , n-1 , 3 . what is the answer ?
A graph is connected iff all nodes can be traversed from each node. For a graph with n nodes, there will be n-1 minimum number of edges.
Given that there are n edges, that means a cycle is there in the graph.
The simplex graph with these conditions may be:
Now we can make a different spanning tree by removing one edge from the cycle, one at a time.
Minimum cycle length can be 3, So, there must be atleast 3 spanning trees in any such Graph.