not use ai please Let G be a disconnected graph which has two components are both are complete: Shouten has st least ((n(n-2))/2) edges. where n is the number ofverties and it is even.

Step 1: It is given that n is even. Let the two components have m and n−m vertices, respectively.…

Answered: Let G be a disconnected graph which has…

Algebra for College Students

10th Edition

ISBN:9781285195780

Author:Jerome E. Kaufmann, Karen L. Schwitters

Publisher:Jerome E. Kaufmann, Karen L. Schwitters

Chapter8: Functions

Section8.4: More Quadratic Functions And Applications

Problem 59PS

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Using the table from Exercise 5, sketch the graph of 2x+3y=12.
Graph: 3x+2y6.
Let G be a simple graph with nonadjacent vertices v and w, and let G+e denote the simple graph obtained from G by creating a new edge, e, joining v and w. Prove that x(G) = min{x(G+e), x((G+e) 4e)}.
Count the number v of vertices, the number e of edges and the number f of regions (face) of each graph and verify Euler's formula. Also find the degree of the outside region| (b) (c) k
Let G be a simple undirected graph. Prove that (a) if G is disconnected, then d(GC) ≤ 2; (b) if d(G) > 3, then d(Gº) < 3; (c) if d(G) = 2 and A(G) = v - 2, then ɛ ≥ 2v - 4.
4. Use g(x) = 3x² - 12x+14 to complete the following. a. Identify the vertex symbolically b. Write g(x) in the form g(x) = a(x – h)? + k (show your work) c. Sketch a graph
Use the formula deg(v) = 2|E(G)| to find the number of edges of the following vЄV (G) graphs. Classify (count) the vertices by number of neighbors. (a) V(G) = [100]. Edges: for all n and m in [100], n ‡ m, n is adjacent to m if and only if |nm| ≤ 4. (b) V(G) = [10] × [10]. Edges: for all (a, b) and (c,d) in [10] × [10], (a, b) ‡ (c,d), (a, b) is adjacent to (c,d) if and only if a = c or b = d. (c) V(G) = [10] × [10]. Edges: for all (a, b) and (c,d) in [10] × [10], (a, b) ‡ (c,d), (a, b) is adjacent to (c,d) if and only if |ac| + |bd| = 1. (d) V (G) = [10] × [10]. Edges: for all (a, b) and (c,d) in [10] × [10], (a, b) is adjacent to (c,d) if and only if |a - c + b-d ≤ 2. (a, b) ‡ (c,d),
Please answer it as soon as possible
5. Let G₁ = (V₁, E₁1) be the following graph. We will show that it is not planar in three ways. E D F H G B (a) Find a subgraph that is isomorphic to a subdivision of either K5 or K3,3. Be sure to label the vertices! (b) Assume on the contrary that G is planar. Find V₁ and E₁, and use only these to explain that G is not planar. (c) Assume on the contrary that G is planar. Use Euler's Formula to find the number of faces and explain that G is not planar (hint: think about how we showed K is not planar)
(h) Suppose that G is an unconnected graph that consists of 4 connected components. The first component is K4, the second is K2,2, the third is C4 and the fourth is a single vertex. Your job is to show how to add edges to G so that the graph has an Euler tour. Justify that your solution is the minimum number of edges added.
Please don't provide handwritten solution ....

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Let G be a disconnected graph which has two components are both are complete: Shouten has st least ((n(n-2))/2) edges. where n is the number of verties and it is even.