The number of edges in a complete bi-partite graph Km.n is equal to n2 whenever а. m>n O b. m< n. O c. m=n=2 d. Non of the choices е. m=n

Q: 4. Consider the following graph. ez es a. How many paths are there from v to vy? b. How many trails…

A: Image is attached with detailed solution.

Q: QUESTION 14 Total number of edges of a complete graph which has 9 vertices is None 36 edges 12 edges…

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Q: 0 1 1 0 0 0 0 0 1 1 1 1 1 1 1 1

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Q: Of the De AJKL has vertices J(2, 3), K(4, 5), and L(6, 1). Graph and label the vertices of AJKL and…

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Q: Q1- What is the minimum distance between points C and F? Q2- Which of the following is a…

A: Given: Q1) To find the minimum distance between points C &amp; F Q2) To find a Hamiltonian circuit…

Q: When K100 and C47 share exactly 20 vertices, all of which are consecutive in C47, how many edges…

A: Total number of edges in K100 = (100*99)/2          =  4950 Total number of edges in C47  = 47 If…

Q: b. a. d. c.

A: Solution:

Q: Person 1 shared a package of graph paper with 3 friends. Person 1 gave 1/4 of the pack to Person 2.…

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Q: d) The number of vertices of degree 4 is. e) The sum of the degrees of G is.

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Q: 2. How many edges has each of the following graphs: (а) (5 рoints) К10: (b) (5 рoints) K,7; (c) (5…

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Q: 22.

A: Note: As per bartleby instruction when more then one question is given only one has to be answered.…

Q: Which of the following graphs have Euler circults or Euler trals? OA: Has Euler trail. DA: Has Euler…

A: Solution: Given that

Q: 17. How many edges has each of the complete bipartite graph K5,13? A. 65 B. 75 C. 55 D. 45

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Q: 4. Count the number of vertices, edges, and faces, and then verify Euler's Formula for the given…

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Q: are both incident with vertex w and z. Based on the graph below, the edges ez es ez ea e10 eg e b.…

A: Graph theory

Q: Which of the following graphs have Euler circuits or Euler trails? K K I I N N P |B: Has Euler…

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Q: 1 Compute the exact value of the length of the graph of g(y) = 20 from y = 1 to y = 2.

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Q: Draw the union of the two simple graphs assuming edges with the same endpoints are the same. а f b f…

A: To explain the correct answer is given below.

Q: How many cycles of length 4 (i.e. 4 edges) are in the complete graph Kg? Note: the cycle 1-2-3-4-1…

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Q: 14. For each of the following figures, find V+F- E, where V, E, and F stand, respectively, for the…

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Q: Find the shortest path from vertex s to all other vertices of the given graph. 2 а b 3 8 6 7 1 S с 4…

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Q: Based on the graph below, what type of edges are eg and e,? e3 es eg e10 b. e12 e6 es e7 S a…

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Q: Q 19 If a fault cuts three sides of a quadrilateral, then: Red with one of the vertices 2- Cut the…

A: Given question:- 19) if a fault cuts three sides of a quadrilateral then,

Q: 28. The complete graph with six vertices has k edges where k is A. 30 B. 15 C. 16 D. 14

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Q: 11. For the 2 graphs below: Which graphs have an Euler circuit? For graph(s) with Euler circuit,…

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Q: ou are working in an organization and it's your primary responsibility to understand the below graph…

A: An edge e is said to be incident on a vertex v if e has one of its endpoints as v. In the given…

Q: Indicate if each of the two graphs are equal Figure 3: An undirected graph has 5 vertices. The…

A: To Find: Indicate if each of the two graphs are equal

Q: An te gr a) Draw K, for n = 1,2,3,4,5. For each, how many edges are there?

A: a)

Q: What is the smallest number of colors you need to properly color the vertices of a Km,n graph? What…

A: Consider the lemma: A bipartite graph with at least one edge has chromatic number 2. It is known…

Q: A connected graph with 12 edges divides a plane into 4 regions. The number of vertices in this graph…

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Q: For which values of n ≥ 0 are the following graphs bipartite? a) Cn b) Wn c) Kn d) Qn

A: A bipartite graph is a graph whose vertices can be divided into two disjoint and independent sets U…

Q: Refer to the graph attached, and answer the following 1. How many vertices are there? 2. How many…

A: A graph is attached, and we need to find answer to the following questions. 1. How many vertices are…

Q: 1. Use the image below to answer the following questions. y es ez e1 e2 a. Name the vertices that…

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A: Remark: A path in a graph is a sequence of vertices with the property that each vertex in the…

Q: Which edges shown on the graph to the right are not included in the following path? F. F. D. C, B, A…

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Q: QUESTION 11 Total number of edges of a complete graph which has 9 vertices is None 18 edges 12 edges…

A: The total number of edges in complete graph of n vertices are (n(n-1))/2

Q: For each of the graphs :(i) Find all edges that are incident on y1.(ii) Find all vertices that are…

A: (1) Edges incident on v1:{e1, e2, e3}

Q: Explain why the graph shown to the right has no Euler paths and no Euler circuits. A D H. Choose the…

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Q: A planar graph has faces (including the external face) composed of eight 3-cycles and eighteen 4-…

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Q: Which of the following edges do we need to add to make the following graph ergodic? 3 4 O 2->3 O…

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Q: 4.Suppose the city of Königsberg had the arrangement of islands and bridges pictured on the left…

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Q: In order to eulerize the graph below, give the fewest number of edges that need to be duplicated. a…

A: Label the vertices of the given graph. Next we use the process of eulerization of the graph by…

Q: For parts (a) and (b), indicate if cach of the two graphs are equal. Justify your answer. bc b a a…

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Q: List all reduced subgraphs with 4 vertices for the following graph. e2 €3 e6 €4 e5 d e7

A: A graph H is called a sub-graph of G if, VH⊂VG EH⊂EG IH is the restriction of IG to EH

Q: Determine which of the graphs below have Euler circuits. Vo Vg VI 3 m (US S 5 e6 4 33 V3 Ug (US 27…

A: Euler circuit: An Euler circuit starts &amp; end at same Vertex Here in the given problem we have to…

Q: Based on the graph below, are vertices z and x adjacent? es ez ez e10 eg es e12 e6 es e7 S True…

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Q: 4. In the figure above, how many paths are there along the edges from point A to point G where the…

A: Given,

Q: give 5 graphs with a bond: with I edge 2 edge 3 edğe 4 edge 5 edge

A: To draw the graph with 1 edge, 2edges , 3 edges, 4 edges, 5 edges

Q: For which values of m and n does the complete bipartite graph Km,n have an Euler circuit?

A: Definitions: A Path in a directed graph G is sequence of edges in G. A Simple path is a path that…

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.