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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.
The ratio of the sum of first n terms of two AP's is 7n+1:4n+27. Find the ratio of their 11th terms . Ans: Let a 1 , a 2 ... and d 1 , d 2 be the I terms are Cd's of t
Compute the dot product for each of the subsequent equation (a) v → = 5i → - 8j → , w → = i → + 2j → (b) a → = (0, 3, -7) , b → = (2, 3,1) Solution (a) v →
what is 5 squared 2
A function is a relation for which each of the value from the set the first components of the ordered pairs is related with exactly one value from the set of second components of t
Q. How to Convert decimals to fractions? Ans. Note: This tutorial covers only terminating decimals.
x=-3(y-2)^2+4
what is number of quadratic equation that are unchanged by squaring their roots is There are four such cases x 2 =0 root 0 (x-1) 2 =0 root 1 x(x+1)=0 roots 0 and 1
Equivalent or Equal sets Two sets C and D are said to be equal whether every member of set C belongs to D and every member of set D belongs also to C.
can you help me? cause im in 7th grade advanced math and tomorrow I have a test tomorrow and I don''t get this
Determine if the acceleration of an object is given by a → = i → + 2 j → + 6tk → find out the object's velocity and position functions here given that the initial velocity is v
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