1. Given an undirected graph G = (V, E), and define a distance function d: V x V → R20 which assigns a non-negative real number to each pair of vertices satisfying d(u, v) = d(v, u). (a) Write down the rigorous mathematical definition for the diameter of G. (b) Write down the rigorous mathematical definition for the radius of G. (c) If d(u, v) is a metric (that is, it further satisfies the triangle inequality: d(x, z) ≤d(x, y)+d(y, z)), prove that the diameter of G is at most two times the radius of G.

Q: Consider the following graph. • V(G) = {v1, v2, v3, v4}, e(G) = {e1, e2, e3, e4, e5}, E(G) = {(e1,…

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Q: 2. (§1.1) Sketch the following set of points in the x-y plane. {(x, y) = R²: (y - x²) (y + x²) < 0}.

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Q: Let R denote the rectangle with corners (−1, −2), (4, −2), (4,1), and (-1,1), and let P denote the…

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Q: Here let A, B, C, and D be four distinct points in the plane. Now supposedly that no three of them…

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Q: 4) Let f(x)=(x+3)squared−4 , give the: a) vertex   b) axis    c) domain    d) range   e) graph

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Q: If the points (h, 0), (a, b), and (0, k) lie on a line, show that 1 + k h

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Q: 1. Determine whether each of the following equations defines y as a function of x. a) x² + y² + 3x=0…

A: Solve : we can write as expicitlySo y is combination of two function so it not represent a…