show that a simple planar connected graph with 17 edges and ten vertices cannot be properly colored with two different colors.

Q: Give an example of a graph with 5 vertices that does NOT have a Hamiltonian circuit. Explain why…

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Q: Suppose there are 10 points in a plane such that no three points are collinear. How many distinct…

A: Given; There 10 points in a plane such that no three points are collinear

Q: If the edges in a path are distinct, it is called:a) simple pathb) simple graphc) length of the…

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Q: If a graph has 5 edges, how many vertices does it have?

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Q: Draw a complete graph with 4 vertices

A: A complete graph is directed a directed graph in which any two vertices are joined by a unique edge.…

Q: 2. Show that any graph with at most 8 vertices is planar.

A: Topic:- planer graph

Q: Construct a non planar graphs

A: A non-planar graph that is not homeomorphic to K5 and K3, 3:

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: Define maximum number of edges in a simple connected graph with n vertices.

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Q: Suppose a graph, G, has five vertices with degrees 9,8,6,5,4. How many edges does G have?

A: We have to find the number of edges in graph G.

Q: . How many nonisomorphic directed simpe graphs are there with 4 vertices?

A: According to the given information, it is required to find number of non-isomorphic directed simple…

Q: 2. Is it possible for a connected graph with 7 vertices and 11 edges to be drawn so that no edges…

A: (2) Consider the provided question, Graph with no edges crossing means that it should be a planar…

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: Show that any graph with two or more nodes and no self-loops contains two nodes that have equal…

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Q: Construct a simple graph with vertices L, M, N, O, P, Q whose degrees are 1, 2, 4, 3, 4, 2 What is…

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Q: Suppose a connected planar graph G has 27 vertices. How many edges must G have if there are 16…

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Q: Suppose you colored edges of a graph either red or blue (not requiring that adjacent edges be…

A: According to the given information, Let the edges of the graph be coloured with red or blue. It is…

Q: Suppose that we have a graph with at least two vertices. Show that it is not possible that all…

A: Suppose, we have a graph with at least two vertices.

Q: A graph with eight vertices and seven edges is not connected. True False

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Q: a simple disconnected graph with 3 vertices.

A: This is an example of simple disconnected graph with three vertices.

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: Prove that a graph with at least three vertices is connected if and only if at least two of the…

A: A graph G is a pair of sets V and E where the elements of the non empty set V are called the…

Q: If we have two different non-crossing drawings of the same connected graph, is it possible for the…

A: The given question is related with planar graphs. Suppose we have two different non-crossing…

Q: Construct a simple graph that is a forest with vertices B,C, D, E, F,G, H,I such that the degree of…

A: "Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: There are 8 vertices namely: A, B, C, D, E, F, G, H Make or draw a graph with 2 loops around the…

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Q: We say that two graphs are distinct if and only if these two graphs are not isomorphic. How many…

A: Given: Two graphs are distinct if and only if these two graph are not isomorphic. To find: How many…

Q: Write an example of three graphs (each with 4 vertices), two of them are isomorphic and two are…

A: We will draw three graphs on four vertices among which two are isomorphic and two are non…

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: A planar graph with 4 vertices with the same degree 5, has 8 faces Select one: True False

A: Solution

Q: Show that any connected simple planar graph on n vertices must have at most n/2 vertices of degree…

A: Consider the equation

Q: 2.29. Is this graph planar (the edges cross each other in the middle but there is no vertex there)?

A: Planar graph: When a connected graph can be drawn without any edges crossing it is called planar.…

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: The graph with 5 vertices and four edges is always connected. TRUE OR FALSE

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Q: The maximum number of edges in a bipartite graph on 15 vertices is ____.

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Q: Can a simple graph exist with 9 vertices all of degree 5?

A: Handshaking lemma: In any graph, sum of degree of all the vertices is twice the number of edges…

Q: How many edges are there in a 3-regular graph with 8 vertices?

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Q: Is it possible to have a graph that only has the form of a "simple graph"? Like it will not have a…

A: A simple graph is a graph having no loops or parallel edges. It also do not posses any directions…

Q: A graph with 4 vertices.

A: This question is related to Descrete Mathematics

Q: Write an example of three graphs (each with 4 vertices), two of them are isomorphic and two are…

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Q: If a graph has 12 vertices with odd degree (valence), what is the smallest number of edges that…

A: At least 6 edges would have to be needed. You would want to add an edgeto each vertex that has odd…

Q: If a graph has 14 vertices with odd degree (valence), what is the smallest number of edges that…

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Q: Can a simple graph exist with 15 vertices each of degreefive?

A: Given problem "Can a simple graph exist with 15 vertices each of degree five?"

Q: A connected planar graph has 13 vertices and 20 edges. How many regions are formed when the graph is…

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Q: Construct a simple graph with vertices N,0, P,Q, R, S whose degrees are 5, 1, 2, 3, 3, 2 What is the…

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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…

Q: How many edges are there in a 3-regular graph with 14 vertices?

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Q: no of edges for a tree with number of vertices 10 is

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Q: Find a self-complementary graph with 8 vertices.

A: We know the definition of Complement of a graph, The complement of a graph G is a graph G' on the…

Q: . Which complete bipartite graphs Km,n, where m and n positive integers, are trees? are

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