Can some one please help me with this two
questions.
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Can some one please help me with this two questions. Thank you! fact that every planar...
Q3.a) Show that every planar graph has at least one vertex whose degree is s 5. Use a proof by contradiction b) Using the above fact, give an induction proof that every planar graph can be colored using at most six colors. c) Explain what a tree is. Assuming that every tree is a planar graph, show that in a tree, e v-1. Hint: Use Euler's formula Q3.a) Show that every planar graph has at least one vertex whose degree...
Please help me solve this discrete mathematical problem and I will gladly give a thumbs up... thanks! Complete the following proof using mathematical induction on the number of vertices, proving that the chromatic number of a connected planar simple graph (CPS) is no more than 6. Justify each step. Basis step: A CPS graph with 6 or fewer vertices is 6-colorable. Inductive hypothesis: Any CPS graph with k2 6 vertices is 6-colorable. Inductive step: Consider a CPS graph with k+1...
can you please help me with these two questions. thank you Explain the second law of thermodynamics and how it related to trophic levels and energy pyramids in systems. Use an example. Explain how biotic factors regulate population abundance. Describe what kinds of biotic factors regulate populations. Give an example.
can someone help me with this two questions please thank you 4. Find a recurrence relation (with initial conditions) for an, the number of ternary sequences of length n that do not contain three consecutive digits that are the same. That is, the patterns '000','111', 222 must not appear anywhere in the sequence. So, 0011012 is acceptable, but 000022 and 1000112 are not. 5. Elsa is making trains out of colored train cars: the red cars are 2 inches long,...
please help me make this into a contradiction or a direct proof please. i put the question, my answer, and the textbook i used. thank you also please write neatly proof 2.5 Prove har a Simple sraph and 13 cdges cannot be bipartite CHint ercattne gr apn in to ertex Sets and Court tne忤of edges Claim Splitting the graph into two vertex, Sets ves you a 8 Ver ices So if we Change tne书 apn and an A bipartite graph...
Please help me with these questions!. Will give thumbs up thank you!
can some please help me understand this question and also if it can be handwritten not typed thank you so much Let U be any set. Prove that for every B ∈ ℘(U) there is a unique D ∈ ℘(U) such that for every C ∈ ℘(U), C \ B = C ∩ D. This problem is similar to Examples 3.6.2 and 3.6.4 and to Exercise 8 in Section 3.6 of your SNHU MAT299 textbook.
Please answer question 2. Introduction to Trees Thank you 1. Graphs (11 points) (1) (3 points) How many strongly connected components are in the three graphs below? List the vertices associated with each one. 00 (2) (4 points) For the graph G5: (a) (0.5 points) Specify the set of vertices V. (b) (0.5 points) Specify the set of edges E. (c) (1 point) Give the degree for each vertex. (d) (1 point) Give the adjacency matrix representation for this graph....
Can you please help me with these questions. 1). Maximize P subject to the given conditions. P = 6x − 7y x ≥ 0 y ≤ 3 x − y ≤ 4 maximum value P = point where maximum occurs (x, y) = 2). Find the coordinates of the vertex of the graph of the equation y = 1/2x2 − x + 2. (x,y) =
please help me with this assignment and show all the work. thank you! Determine if each set countable or uncountable. Show a proof or argument to justify your decision for each set. a) the ages of students in this class b) the integers that are multiples of 10 c) Real numbers between and including 4 and 6 [4,6]