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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.
Find the lesser of two consecutive positive even integers whose product is 168. Let x = the lesser even integer and let x + 2 = the greater even integer. Because product is a k
how to divide fractions?
64% of the students within the school play are boys. If there are 75 students in the play, how many are boys? To ?nd out 64% of 75, multiply 75 by the decimal equivalent of 64%
my daughter in kg now how can i train her to develop skills in undertanding the basics of all subjects how can i start teaching other than schol
Find the probability of drawing a diamond card in each of the two consecutive draws from a well shuffled pack of cards, if the card drawn is not replaced after the first draw
Differance between Expanded Notation vs. Standard Notation ? A number written in expanded notation is broken down into parts just like it is in a place-value table. Example
rajan bought an armchair for rs.2200 and sold it for rs.2420.find his profit per cent.
what is the differeance in between determinate and matrix .
HE IGHTS AND DISTANCES If the angle of elevation of cloud from a point 'h' meters above a lake is α and the angle of depression of its reflection in the lake is β , prove
111111-11111=
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