1. (a) What is the maximum number of edges that a bipartite planar graph with 10 vertices can have? Give a planar drawing of a bipartite graph attaining this number of edges. (b) If a connected planar graph with n vertices, all of degree 4, has 10 regions, determine n. Give an example of such a graph.

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: Suppose now we allow negative edge weights. Then we can get a graph of score (2,0,0), which is of…

A: Given that, we allow negative edge weights. Then we can get a graph of score (2,0,0), which is of…

Q: Is hypercube graph Q4 planar? If not can you provide any bounds on it crossing number?

A: No, hypercube graph Q4 is not a planner graph.

Q: 4. Prove: "Show that the number of edges in a simple planar graph of order n is at most 3n – 6".…

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Q: Show that the maximum number of edges in a graph with n-vertices is *C2 (d)

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Q: Suppose G is a simple graph (no loops; no parallel edges) with n = 14 vertices and m = 7 edges. What…

A: GIVEN  vertices n=14 edges m=7 EXPLANATION as we know  every graph has atleast n-m component…

Q: Can we draw a planar graph with n= 7 and e = 12 such that each region is bounded by exactly 3-edges…

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Q: If a simple disconnected graph has 7 vertices and 2 connected components what is the maximum number…

A: Given question is If a simple disconnected graph has 7 vertices and 2 connected components what is…

Q: 9. Draw two simple connected undirected graphs, each with six nodes, with every node of degree 3,…

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Q: A graph G has 15 edges, three vertices of degree 4, two of degree 1 and the remaining vertices have…

A: We are given with the number of edges and we know that the number of degrees is equal to twice of…

Q: Give an example of a graph G of order 6 and size 10 such that the minimum and maximum degree of a…

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Q: A box with a square base volume of 1500 cm^3 is to be constructed by taking a piece of cardboard 20…

A: Given that, A box with a square base volume of 1500 cm^3 is to be constructed by taking a piece of…

Q: What kind of graph (from Table 1) can be used to modela highway system between major cities wherea)…

A: To find- What kind of graph (from Table 1) can be used to model a highway system between major…

Q: Suppose a planar graph G is not connected and has exactly 2 components. What is the value of n – m+…

A: To obtain the result, use Euler's formula for planar graphs. Let G be a connected planar graph with…

Q: Among each pair of the CEOs of N companies there is (a) mutual like; (b) mutual dislike; (c) neutral…

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Q: An edge is called a bridge if the removal of the edge increases the number of connected components…

A: We draw a graph without loop, find number of bridges by removing edges.

Q: (7) Verify whether it is possible to have a connected Eulerian graph with 3 vertices and 6 edges,…

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Q: Draw an undirected graph that has exactly 11 edges and at least 5 vertices, in which two of the…

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Q: Show that a finite simple graph with more than one vertex has at least two vertices with the same…

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Q: The graph G₁ has 6 vertices, all of degree 3. How many edges does G₁ have? The graph G₂ has 8…

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Q: 11. Either draw a graph with the specified properties or explain why no such graph exists. (1) Graph…

A: As per our guidelines I am solving only 1st 2. For others kindly resubmit the question mentioning…

Q: The complete tripartite graph K,, consists of three sets of vertices (of sizes r, s and t), with an…

A: Given that The complete tripartite graph Kr,s,t The graph of K2,2,2 in the following graph Hence,…

Q: You have a simple graph G with three vertices and three edges. How many subgraphs can be made from…

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Q: 3. (MS) Select all that are true. a. Every graph has a vertex cover of size 0. b. Every graph has a…

A: Vertex cover V' of an undirected graph G=V,E is defined as a subset of V such that  if uv∈E implies,…

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

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Q: Let G be a simple connected plane graph with 6 vertices. (a) (b) (c) (d) What is the largest number…

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Q: 19 Can a graph with three vertices of degrees 2, 1, 4 exist? Yes No

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Q: Construct a graph with vertex connectivity=3 edge connectivity=4 and minimum degree of a vertex is 5

A: We need to construct graph.

Q: 1. Say two methods for testing the non planarity of graphs.

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Q: Draw a directed graph with as few edges as possible that is strongly-connected, has 8 vertices of…

A: Strongly connected directed 8 vertices one has in-degree 3 two have cut degree 3 rest have samller…

Q: Do the following: 1. Find a graph with 12 edges having six vertices of degree three and the…

A: We need to find a graph with 12 edges, such that 6 vertices have degree three and remaining all the…

Q: 1. Create a connected graph having 6 vertices and 11 edges. 2. Label vertices with A,B,C,D,E and F.…

A: Given: 1) Create a connected graph having 6 vertices and 11 edges 2) Lable vertices with A, B, C, D,…

Q: If a graph has 8 vertices with odd degree (valence), what is the smallest number of edges that would…

A: Solution is done in step 2

Q: Either draw a graph with the specified properties or explain why no such graph exists. Graph with…

A: As 3 questions are given , I will solve only the first question, 1.Graph with five vertices of…

Q: 2. Suppose G is a planar graph having 67 edges. If each face of G has length at least 6, then what…

A: From the given information. The number of edges (e) = 67 The number of vertices at each face (v) = 6

Q: Suppose a graph G has 22 vertices. What is the minimum number of EDGES that G must contain if Diracs…

A: Dirac's theorem Let G = (V,E) be a graph with n vertices in which each vertex has degree at least…

Q: A graph with 20 edges and each of the vertex having degree 4. Find the number of vertices of the…

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Q: 13. A connected graph with six vertices and six edges. tree with five vertices cal degree of 6.,

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Q: If a graph with six vertices is embedded in S?, what is the maximum number of edges it can have.…

A: Consider the provided question, A graph G is embedable on S2 if it is embedable on a plane. Since,…

Q: A simple graph has 6 vertices and 12 edges. Each vertex has degree either 2 or 5. How many vertices…

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Q: If a graph with six vertices is embedded in S², what is the maximum number of edges it can have.…

A: I have Provided this answer in step-2.

Q: Consider graphs with 9 vertices. What is the maximum number of edges in the graphs with Eulerian…

A: In a graph theory, Eulerian trail is a trail in a finite graph that visits every edge exactly once.…

Q: G is a graph on 6 vertices with exactly

A: (b) G is a graph on 6 vertices with exactly two biconnected components:

Q: 1. Find a graph with 12 edges having six vertices of degree three and the remaining vertices of…

A: As per the company rule, we are supposed to solve one problem from a set of multiple problems.…

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: If G is a (not necessarily simple) graph with n vertices where each vertex has degree greater than…

A: Definitions: Simple graph: A simple graph is an undirected graph with no parallel edges and…

Q: Let G be a graph with n vertices and an independent set of size s ≥ 1. What is the maximum possible…

A: Please check the next step for details

Q: Provide an easy-to-understand explanation for the direct proof problem below: For every graph that…

A: Given, for every graph that is undirected (no self-loops or multi-edges) with n nodes.

Q: 2) Find, with a proof, the number of distinct graphs with vertex set [n].

A: 2) The number of distinct graphs of vertex set for given n should be found. Let us take n=3.…

Q: A graph contains 45 vertices. If two vertices have the same degree, they are not connected by an…

A: The graph has 45 vetices and it has two vertices of same degreebut they arre not connected by an…