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Prove that a simple graph is connected if and only if it has a spanning tree.
Ans: First assume that a simple graph G has a spanning tree T. T consists of every node of G. By the definition of a tree, there is a path among any two nodes of T. As T is a subgraph of G, there is a path among each pair of nodes in G. Hence G is connected.
Here now let G is connected. If G is a tree then nothing to prove. If G is not a tree, it must consist of a simple circuit. Let G has n nodes. We can choose (n - 1) arcs from G in such type of a way that they not form a circuit. It results into a subgraph comprising all nodes and only (n - 1) arcs. So by definition this subgraph is a spanning tree.
I am a number yell my identity subtract 20 from me and add 30 make the total twice to reach century you still need eight
200000+500
what is answer ? + 5=10+5
IN THIS WE HAVE TO ADD THE PROBABILITY of 3 and 5 occuring separtely and subtract prob. of 3 and 5 occuring together therefore p=(166+100-33)/500=233/500=0.466
hi i would like to ask you what is the answer for [-9]=[=5] grade 7
Q. Sum and Difference Identities? Ans. These six sum and difference identities express trigonometric functions of (u ± v) as functions of u and v alone.
Linda bought 35 yards of fencing at $4.88 a yard. How much did she spend? To multiply decimals, multiply generally, count the number of decimal places in the problem, then us
verify liouville''s theorem for y''''''-y''''-y''+y=0
1.A=the set of whole numbers less tan 4 ? 2.B=the set of prime numbers less than 19 ? 3.C=the set of first three days of week?
The number of seats in each row can be modeled by the formula C_n = 16 + 4n, when n refers to the nth row, and you need 50 rows of seats. (a) Write the sequence for the numb
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