Doubts in MCQ's

#1

Time Complexity Of Kruskals Algorithm(Here E is the number of edges and V are the number of vertices)
a) O(ElogV)
b) O(Elog√E)
c) O((V^2)log(E^2) + Elog(V^2)) d)
d) O(ElogE + Elog(V^2))

how is d correct

Q2How many undirected graphs (not necessarily connected) can be constructed out of a given set V= {V 1, V 2,…V n} of n vertices ?
ans why 2^n is not the soln
if not connected then it can have nco +nc1 + nc2 —ncn

QHow many simple undirected non-isomorphic graphs are there with 4 vertices
how 64 is the answer

#2

for Kruskals Algorithm time complexity go through the video lecture… prateek bhaiya has explained it over there…

#3

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#4

Sorry but my doubt is not clear yet,
Firstly i know E is proportional V square but still what property of log in giving d as correct option
And also other mcq’s are not answered yet. Please see to it at your earliest

#5

The time complexity for Kruskal’s algorithm is O(ElogE) or O(ElogV). Here, E and V represent the number of edges and vertices in the given graph respectively. Sorting of all the edges has the complexity O(ElogE). After sorting, we apply the find-union algorithm for each edge. The find and union operations have the worst-case time complexity is O(LogV). So overall complexity becomes O(ElogE + ElogV). The value of E can be V^2 in the worst case.

#6

In an undirected graph, there can be maximum n(n-1)/2 edges. We can choose to have (or not have) any of the n(n-1)/2 edges. So, total number of undirected graphs with n vertices is 2^(n(n-1)/2)