Corollary 5.6. (1) If G is a connected simple planar graph with (n 2 3) vertices and m edges, then m < 3n (ii) If in addition, G has no triangles, then m < 2n – 4. 6.

Q: The figure below shows a graph of the function of f((1)) in the coordinate plane. Vertex: Axis of…

A: For a parabola that opens down, the vertex is located at the maximum point. Axis of symmetry is the…

Q: 43.) What is the vertex of the graph y = | x | - 6? a. (-6,0) b. (0,6) c. (6,0) d. (0, -6)

A: Consider the standard form y = |x-a| + b Here, the vertex is (a,b)

Q: Optimal solution: Optimal objective value

A: We have the minimum  value of z=3x−ythe optimal  solution and optimal objective function value:…

Q: Which is not a point on the graph of 2x + 3y - z -12 = 0? a. (6,0,0) b. (3,3,3) c. (0,4,0) d.…

A: Substitute 6,0,0 for x,y,z in the equation 2x+3y-z-12=0. 26+30-0-12=012+0-0-12=00=0 Since points…

Q: Based on K1, K2, and K3, which graphs are simple graphs? y K1 2 K2 2 K3 z K, and K2 a K2 and Kg K1…

A:

Q: 2n 4. Prove or disprove: for every n-vertex graph G, x(G) ≤ 2w(G) + a (G) (6 + 10.

A: There is n -vertex graph G. For the n vertex graph G, it has to be proven that χ(G) ≤2ω(G) + 2n/α(G)…

Q: Determine whether (1,1) is included in the graph. 2x+6y <9 Is (1,1) included in the graph?

A: 2x+6y&lt;9 We need to determine weather (1,1) is element of 2x+6y&lt;9. Now look at 2*1+6*1=8&lt;9.…

Q: 2.1 For each of the following statements, find a graph with the required property and draw it. (a) A…

A:

Q: When n = 3, there are nonisomorphic simple graphs.

A:

Q: 16.) What is the vertex of y = | x | - 5? a. (5,0) b. (-5, 0) c. (0, 5) d. (0, -5)

A: Let's Consider a standard form for the given absolute value equation: y = |x -a| + b The equation…

Q: V8 00000 V7 B. 02 C. V3 5 D. VA E. 05 V6 3. Let S = {₂}. Which of the following vertices are in…

A:

Q: 2.15 Find a graph G with 10 vertices, 24 edges and Y(G) = 4. 10 2193

A: Given information: Number of vertices: 10 Number of edges: 24 Domination Number: 4 Dominating set: A…

Q: 4a Let n > 4. What is the maximum possible number of edges in a graph with n vertices and n-2…

A:

Q: 18.) What is the vertex of y = |x - 3| + 5?

A: Given experssion is , y=x-3+5

Q: is the graph of y = -2/3 x + 4. -6-5-4-3-2-10 1 2 3 456 -1 -2 -3 -4 -5 -6 65 321

A:

Q: Sketch the graph of y = (x + 1)ʻ – 5. | Hint: Is the x-coordinate of the vertex positive or…

A: we have given function y=x+12-5 we have to draw the graph of the above function put x=0 then we get…

Q: 4.1) (R.4) Please provide the graph for Go F. 4 G 2

A:

Q: What kind of symmetry do the following graphs have, if any? (3) (4) 1. (5) (6)

A:

Q: 5. on the space provided. Vertex Opening Equation Graph 1. 2. y=4-x2 4. 3. y (x+5)2 6. y 1+3(x- 6)²

A:

Q: nl.ca/d21/le/dropbox/520780/171312/DownloadAttachment?fi 5. Graph using the vertex and intercepts..…

A: Given parabola is y=-x2-4x-4

Q: G14. Draw two 'different' graphs with five vertices and degrees {1, 2, 2, 2, 3}.

A:

Q: 8. Graph 3y = 9x - 6.

A:

Q: 18 -18 10 -10 A) P(x) = x3 + 4x2 -x-5 C) P(x)=x5 + 43 - x2 + 3x – 5 B) P(x) =x3 + x2 +x+5 D) P(x) =…

A: Given query is to find the equation of the graph.

Q: State and prove closed Graph theorem.

A: