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A complete graph on n vertices is an undirected graph in which every pair of distinct vertices is connected by an edge. A simple path in a graph is one in which no vertex is repeated. Let G be a complete graph on 10 vertices. Let u, v, w be three distinct vertices in G. How many simple paths are there from u to v going through w?
discretemathematics
graphtheory
testseries
asked
Jan 24
in
Graph Theory
by
sudharshan
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Is it $720?$
0
i would be much more than that
0
@aditya333
what it should be according to you?
+4
no of vertices total_paths
3 1
4 7C1 * 2!
5 7C2 * 3!
6 7C3 *4!
7 7C4 * 5!
8 7C5 * 6!
9 7C6 * 7!
10 7C7 * 8!
final answer would be summing up all these values
0
When you are taking number of vertices as 3, then it should be $^{10}C_3*3!$ for example when path length is 2(i.e. we have 3 vertices) suppose $u=1,v=2,w=3$ then there are 6 different ways are there.
0
the path starts at u and ends at w. So there is only 1 place to place v that is between u and w
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I am taking vertex set as $V = \{1,2,3,4,5,6,7,8,9,10\}$.
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is it 60621?
answered
Jan 24
by
Sushant Devkar
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