6. (In this problem, y denotes the domination umber of a graph.) Let G be a graph such that (G) > 3. Prove that diam(G) < 2.

Q: For the graph G below, compute x(G) and find a x(G)-critical subgraph.

A: Given Information:The graph is given as follows: (Name the vertices with numerical…

Q: 3) Use the graph of f(x)-Сах to determine values for C and a -3 3

A: It is clear from graph that when x=0 , f(x)=3 , that is f(0)=3, using this , we can calculate C.

Q: Let p (x) = -3(x - 1) (x + 2). Which statement describes the end behavior of the graph of p? O As z…

A:

Q: Use the parameters of a,h,k in h(x)=a|x-h|+k to the graph h(x)=-3|x-1|+4.

A: Given           h(x)=-3x-1+4 First, lets compair with the general form:     h(x)=ax-h+k The value of…

Q: If A = {xeR: 2≤ x ≤5}, B = {xeR: − 2 ≤ x ≤ 1}, C = {xeR: -1 < x ≤ 1}. a) Sketch the graph of Cx…

A: information provided. However, I can guide you through the process of sketching the graphs of the…

Q: consider ihe foriowing polýnomiai functions 2 f(x) =-2x"+8 .hx): 3x(x3ー4) 4 please graph BötH

A:

Q: Use the graph below to answer the following questions:

A:

Q: The following graph of g" has exactly three x-intercepts.a. For what values of x in (-4, 3) is the…

A: Graph : Here given graph of g'' (x) So here inflection point is x intercept of graph g''(x) So…

Q: Let G be a simple undirected graph. Prove that (a) if G is disconnected, then d(GC) ≤ 2; (b) if d(G)…

A: Given: G is a simple undirected graph.To prove: a) d(Gc)≤2 if G is disconnected.                 b)…

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: 1.Show that K3,3 is non planner graph

A:

Q: 7. Prove : Every graph with radius r and girth with 2r +l is regular

A: To Determine :-  Every graph with radius r and girth with 2r +1 is regular.

Q: Both OM 0.287 0.147 0.716 Neither 0.144

A: Solution

Q: In Problem ,draw a complete graph so that it has the type of symmetry indicated.

A: Given that, This is the graph is an upper horizontal half parabola whose vertex at -4, 0 crosse…

Q: Select the graph for which a) ƒ¹(x) > 0 and f11(x) > 0

A: It is given that, the f'(x)&gt;0 Which means the function f(x) is increasing.Therefore Graph-a is…

Q: .-) oketen a graph of p(x) =-21x-11 + 4 2 12 6-5 -4 -3-21 1 2 3 456 2 4 0-3 5 6 7. Given f (x) x24,…

A: As per norms, the three subparts a, b and c are answered. Questions regarding the functions f , g…

Q: (a) |V(G)| > a(G) · w(G) (b) |V(G)| = a(G) · w(G) (c) |V(G)| < a(G) - w(G)

A: This is a problem of Graph Theory.

Q: 2. Let G and H be a graphs. Prove that if G = H, then H= G.

A: Given: It is given that let G and H be a graphs , the objective is to prove that if and then

Q: Please do the following questions with handwritten working out

A: Question (a): What is the minimum number of connections whose deletion would stop pop-its reaching…

Q: 10) Find the end behavior of the given graph. As x→-00, f(x) As x→ 0, Ht) 恩) 00,

A:

Q: 1) This is the graph of y = g(x). What is the end behavior of g? Choose 1 answer: As x → +o, g(x)…

A: Check the extreme point of graph

Q: 3) Let f(x,y) = 9x² + y² Statch the graph of fl

A: Sketch the graph of f(x,y)=9x2+y2

Q: Skerch graph of ea ch funetion Show wor a. fa)= 4X² - 3x²-90x+23 %3D b fey- 8xe-axリ-2

A: The graph of a function f is the set of ordered pairs, where f(x) = y. In the common case where x…

Q: Prove that for any graph G, y(G) ≤ 2ir(G)-1.

A: Please find the attached solution

Q: = Let G be a graph and e E E(G). Let H be the graph with V(H) = = V(G) and E(H) = E(G)\{e}. Then e…

A: The objective of the question is to determine whether each edge in a given graph is a bridge, and to…

Q: What is the vertex of g (x) = (x + 3)+3?

A:

Q: Determine the domain of the following

A: Given,

Q: Suppose G is a simple connected graph such that G is unicyclic. Prove that |V (G)| = |E(G)|.…

A: A cyclic graph has minimum of 3 vertices which is connected in a cycle and a graph is unicyclic…

Q: Let G be a bipartite graph of order p. Then i(G) ≤ 2.

A: please find the attached image

Q: 1. Give a proof or a counterexample for the statement: for every graph G, x(G)<|V(G)|-a(G)+1. You…

A:

Q: is transformed into the graph of 2y 6 y = f(x) becomes point ( 57, If the graph of y = E(x) -4 f( x-…

A:

Q: The Euler's formula v - e + f = 2 holds for all connected planar graphs. What if the graph is not…

A: The formula for multiple connected component c is, v +f = e + c + 1

Q: 3. Consider the following graphs G₁, G2, and G3 G₁ is the graph with vertex set {1, 2, 3, 4, X5, X6,…

A: Two graph are isomorphic if they have one one onto mapping from vertex and edge set of one graph to…

Q: Create a single graph that has all of the following key features. 1. End behavior: as I -00, f (x) →…

A:

Q: Consider the graph below of y = f(x) and answer the following questions. + -2 -2 -4 a) As a → 2,…

A:

Q: Determine the composition of the following. 29) (f o g)(-5) = Also written as f(g(-5)) = . %3D A) 3…

A: We know that, f∘g(x)=f(g(x)) for two functions f and g. A function f has a local minimum at x∘ if…

Q: Prove that for any two simple connected joint graphs G and H, L(G) UL(H) L(GUH).

A: Introduction: A connected joint graph is a graph formed by connecting two graphs by a single edge.…

Q: 12) Graph h(x) = -3(x+ 2)² + 9 by determining whether its graph opens up or down and by finding its…

A: Given: h(x)= -3(x+2)2+9  Compare the given function with f(x)=a(x-h)2+k. It represents a parabola.…