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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.
We have to enclose a field along with a fence. We contain 500 feet of fencing material & a building is on one side of the field & thus won't require any fencing. Find out the dime
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
sin^2alpha *sec^2beta +tan^2 beta *cos^2alpha=sin^2alpha+tan^2 beta
Advantages And Limitations Of Game Theory Advantage Game theory assists us to learn how to approach and understand a conflict condition and to develop the decision making
Q. Determine the probability of tossing a head? Let B represent the event of tossing a heads with the nickel in example 2. Find P(B). Solution: S = {(H, H), (H, T), (T, H
how do we solve multiple optimal solution
The canister of the nerf super soaker washout holds 22 ounces of water. say you use 1/2 of the water. how much water is left in the canister
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1. Suppose the arrival times of phone calls in a help centre follow a Poisson process with rate 20 per hour (so the inter-arrival times are independent exponential random variables
Example of Cartesian coordinate Graph: Example: The temperature of water flowing in a high pressure line was measured at regular intervals. Plot the subsequent recorded da
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