To write the equation and solve for the unknown and check.

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2. In a computer network some pairs of computers are connected by network cables. Your goal is to set up the computers so that messages can be sent quickly from any computer to any other computer. For this you have identified each of the n com- puters uniquely with a number between 1 and n, and have decided that a message should consist of two such numbers, identifying the sender and the recipient, fol- lowed by the content of the message. As cables are relatively short, you can assume that sending a message across a single cable takes an amount of time that is the same irrespective of the length of the cable. You can further assume that at most one message travels between computer at any point, so that you don't have to worry about inference among messages. (a) Define a graph or network that models the computer network and allows you to answer the remaining parts of this question. (b) Consider two computers, a sender and a recipient. Using the graph or network you have defined,…

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Chapter 45, Problem 31A

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To write the equation and solve for the unknown and check.

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2. In a computer network some pairs of computers are connected by network cables. Your goal is to set up the computers so that messages can be sent quickly from any computer to any other computer. For this you have identified each of the n com- puters uniquely with a number between 1 and n, and have decided that a message should consist of two such numbers, identifying the sender and the recipient, fol- lowed by the content of the message. As cables are relatively short, you can assume that sending a message across a single cable takes an amount of time that is the same irrespective of the length of the cable. You can further assume that at most one message travels between computer at any point, so that you don't have to worry about inference among messages. (a) Define a graph or network that models the computer network and allows you to answer the remaining parts of this question. (b) Consider two computers, a sender and a recipient. Using the graph or network you have defined,…

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1. Let W, U, and S be graphs defined as follows: • V(W) is the set of countries in the world; • V(U) is the set of countries in the European Union; V(S) is the set of countries in the Schengen Area; ● for X = {W,U,S}, E(X) is the set of pairs of countries in V(X) that share a land border. Recall that land borders between countries in the Schengen Area are special in that they can be crossed without a passport. (a) The notions of a country and a land border are somewhat ambiguous. Explain the notions you will use to get a precise definition of the graphs W, U, and S. (b) Is S a subgraph of U? Is U an induced subgraph of W? Justify your answers. (c) Using non-mathematical language, explain what it means for a country x if VEV(S) and dw (v) = 0. Give all such countries. Let A = {v Є V(W) \V(S) such that |Nw(v)| > 0 and Nw (v) ≤ V(S)}. (d) Using non-mathematical language, explain what the set A represents in terms of countries and land borders. Give a specific element of A or explain why A…