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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.
AskIf y=e^(a?sin?^(-1) x), prove that (1 – x2)yn+2 – (2n + 1)xyn+1 – (n2 + a2)yn = 0. Hence find the value of yn when x = 0. question #Minimum 100 words accepted#
product line of lg company
Utilizes the definition of the limit to prove the given limit. Solution In this case both L & a are zero. So, let ε 0 so that the following will be true. |x 2 - 0|
Can we solve the Quadratic Equations by completing the square method? if yes explain it.
(a+b+c)2=
Array - when items are arranged in a regular rectangular pattern of rows and columns, counting how many there are. (e.g., if there are 3 rows of 5 girls each, how many girls are t
Example: Suppose your football team has 10 returning athletes and 4 new members. How many ways can the coach choose one old player and one new one? Solution: There are 10 wa
two circle of radius of 2cm &3cm &diameter of 8cm dram common tangent
01010011 01100101 01101101 01110000 01100101 01110010 00100000 01000110 01101001 00100001
Juan is g years old and Eva is 2 years younger than Juan. a.Find the sum of their ages in terms of g. b.Find the sum of their ages in g years'' time,in terms of g.
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