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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.
is that rational or irrational number
Ask questioOn average, Josh makes three word-processing errors per page on the first draft of his reports for work. What is the probability that on the next page he will make a) 5
show that a*0=a
draw a equilateral triangle with length of side 6.5 cm. and let us draw a parallelogram equal in area to that triangle and having an angle 45 degree
(i may have spelled it wrong)but i forgot how to do them.
compare 643,251;633,512; and 633,893. The answer is 633,512
16 times 4
A two-digit number is seven times the sum of its digits. The number formed by reversing the digits is 18 less than the original number. Find the original number.
What is symmetric value
Let R be the relation on the set of ordered pairs of positive integers such that ((a, b), (c, d)) ∈ R if and only if ad = bc. Determine whether R is an equivalence relation or a p
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