A random undirected graph has 9 vertices. An unordered cycle is a connection within the graph...
A random undirected graph has 9 vertices. An unordered cycle is a connection within the graph that connects a number of vertices. For example an unordered cycle of 3 would be a triangle within the graph of 3 connected vertices. To find the total number of possible unordered cycles of 3 vertices from a total of 9 you can use the Combination Formula C(n,r) = n!/r!(n-r)! which is total number of possible combinations of r objects from a set of n objects. If the probability of an edge between any two vertices is 50% - what is the expected number of unordered cycles?
Homework Answers
We can select 3 vertices from 9 in ways = 9C3=84
Probability that 3 vertices (a,b,c) form a cycle = Probability of
edge between vertices a and b∗ Probability of edge
between vertices b and c∗Probability of edge between vertices c and
a
=0.5*0.5*0.5=0.125
So, expected number of cycles of length 3 = 84*0.125=10.5
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Write a program, IN JAVA, to implement the
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Write a driver program, which reads input file mediumG.txt as an
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