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Graphs and Functions

Prove Let D be a nontrivial connected digraph.

4.4 Prove Let D be a nontrivial connected digraph. Then D is Eulerian if and only if od(v)=id(v) for every vertex v of D. Od means the outdegree of a vertex v of a digraph D. (is the number of vertices of D that are adjacent from v. id means the indegree of a vertex v of a digraph D.( is the number of vertices of D adjace

Self-Complementary Graph Proof

1.10 Let G be a self-complementary graph of order n, where n=1(mod 4) Prove that G contains at least one vertex of degree (n-1)/2 (hint: Prove the stronger result that G contains an odd number of vertices of degree (n-1)/2. Can you explain it step by step and draw a graph.

Graph positive vertices

1.2 Let n be a given positive integer, and let r and s be nonnegative integers such that r+s=n and s is even . Show that there exists a graph G of order n having r even vertices and s odd vertices.

K-connected graph

3.17 Let v_1,v_2,...,v_k be k distinct vertices of a k-connected graph G. Let H be the graph formed from G by adding a new vertex of degree k that is adjacent to each of v_1,v_2,...,v_k. Show k(H)=k. k(G)=is the vertex connectivity

Connectivity for K-Partite Graph

3.16 Determine the connectivity and edge-connectivity of each complete k-partite graph. Can you explain it step by step and draw a graph.

Intercepts of a Line

Find both the X-intercept and the Y-intercept of the line given by the equation - 9x + 4y + 13 = 0

A Nontrivial Connected Digraph

Prove that a nontrivial connected digraph D is Eulerian if and only if E(D) can be partitioned into subsets E_i , 1<=i<=k, where [E_i] is a cycle for each i. <= means less and equal. Please can you explain this step by step and can you draw a graph.

Graphing the Equation Line

Graph the line 9x + 5y = -17 Please make the points visible so I can see them. See the attached file for the full problem.

Strongly regular graph proof

Let n >= 2 be a number. Define the graph L2(n) as follows: Vertices are ordered pairs from the set {1, ..., n}. Two vertices are adjacent if they have the same first coordinate, or the same second coordinate (but not both). Show that this is a strongly regular graph, and find its parameters.

Poisson Random Variables

(a) If X is a Poisson random variable with parameter lambda, show that E[x^n] = lambda(E[(x+1)^(n-1)]) (b) Use this result to compute E[X^3]

Find examples of four types of graphs.

Relate the application to the specific graph (line, parabola, hyperbola, exponential). Describe the characteristics of each application as related to the graph. All of the graphs in this lesson occur in real life. Using the Cybrary, web resources, and other course materials, find a real-life application of each graph. ? R

Piecewise Functions

F(x) = {x if 0<= x <=1} {2-x if 1< x <=2} {0 if x > 2} Define a new function g, whose domain consists of all numbers x such that 0 &#8804; x &#8804; 4, and whose value g(x) for such x is given as follows: g(x) = the area between the graph of the function f and the horizontal axis from 0 to x. Problem: Find a f

Connected Graphs

Let G be a graph of diameter at least three. Can you find an upper bound on the diameter of the complement of G? Prove your findings! Let G be a connected graph and sq(G) be a graph which contains all vertices and edges of G and moreover edges joining every pair of vertices that were in G at distance 2. In other words, xy is

Graphing on the Number Line

Graph, on the number line, all points X for which Mod(X-3)<=3 See attached file for full problem description.

Cancer and Heart Disease : Graphing, Trends and Forecasting

1. Disease 1985 1990 1995 2002 Heart Disease 771169 720058 737563 696,947 Cancer 461563 505322 538445 557,271 2. a. Plot this data for each disease as points in a rectangular coordinate system. b. Using a smooth line, connect your data points for each disease. c. On a separate graph, plot only the years

Finding Slope through Points

Find the slope of the line that goes through each pair of points: (-5, -2) and (-2,1). What is the steepness of the line? (i.e. 3 units up and 5 units right)

Slope-Intercept Form

Determine the equation of the line. Write the answer in slope-intercept form. 52. The line through (4,0) that is perpendicular to the line x + y = 3