A graph whose vertices and edges can be drawn in a plane such that no two of the edges intersect.

Q: © Show that it is not possible to create degree 3 and 2 vertices of degree &. graph with 7 verlices…

A: By handshaking lemma, we get that the sum of degrees of all the vertices in a graph is two times the…

Q: Are these pairs isomorphic? If yes, label the vertexes to show isomorphism. If not, why they are not…

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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: Give a simple example of a connected graph such that an edge (u, v) is a light edge for some cut,…

A: Considering an example of a triangle, whose all weights of edges are equal. This is an example of…

Q: Let G be a simple plane graph with fewer than 12 faces, in which each vertex has degree at least 3.…

A: Step 1: Consider the provided question, (17) (i)

Q: The of a vertex is the number of edges along the unique path between it and the root. Height Degree…

A: The level of a vertex is the number of edges along the unique path between uand the root.

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

A: Topic:- planer graph

Q: A square with two diagonals drawn is a complete graph. True False

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Q: A trail is a walk that does not repeat an edge. Prove that a trail that repeats a vertex must…

A: Assume that vertex Vk is repeated Let the trail be W: V1V2.....Vk........Vn....Vi.....Vk.......Vj…

Q: Let G be a simple connected planaı 13 vertices and 19 edges. Then, the number of faces in the planar…

A: Given that, G is a simple connected planar graph with 13 vertices and 19 edges.

Q: The most famous theorem in graph theorem is the following: Theorem 1. The vertices of a planar graph…

A: No, it is not true that all graphs with χG<4 are planar. it is known that Peterson graph is not…

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: If the results of a two-factor experiment are presented in a line graph, then what pattern appears…

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Q: The of a vertex is the number of edges along the unique path between it and the root.

A: Rooted TreesA rooted tree is a tree in which one vertex has been designated as the root and every…

Q: show that a simple planar connected graph with 17 edges and ten vertices cannot be properly colored…

A: We can solve this using Euler theorem

Q: Draw a bipartite graph with a vertex partition into the two sets {v1, v2, v3, v4} and {v5, V6, v7}…

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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: Use the pigeonhole principle to prove that a graph has at least two vertices with the same degree

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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: Find the image of un der w- 2く

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Q: If countries in the Southeast region are consisting of archipelagos then other foreign countries…

A: Euler diagram is a general diagram giving meaningful information about things that are related to…

Q: The of a vertex is the number of edges along the unique path between it and the root . Child Degree…

A: Here we are given the definition from graph theory. We have to fill the blank with appropriate word…

Q: Which of the following statements about a connected graph is always TRUE?         A path of…

A: Solution: From the definition of the connected graph there should be path between any two pair of…

Q: 2. Show how the graph of Fig. 5.8 can be drawn in the plane without crossings.

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Q: An outerplanar graph is a graph that admits a planar embedding with all vertices on the boundary of…

A: Given that an outerplanar graph is a graph that admits a planar embedding with all vertices on the…

Q: 3. Draw the largest hypercube graphs which is planar.

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

A: Consider the equation

Q: True or False: The edge set of every closed trail in a graph can be partitioned into edge sets of…

A:

Q: 3 5

A: Isomorphism of graph: Let G and H be two graphs. They are said to be isomorphic if there exists a…

Q: Prove that cycles are bipartite for an even number of vertexes. But they are not bipartite for the…

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Q: How many regions of the plane are formed by the graph below:

A: When a planar graph is drawn without edges crossing, the edges and vertices of the graph divide the…

Q: determine thesum of the in-degrees of the vertices and the sum of theout-degrees of the vertices…

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

Q: show that every simple finite graph has two vertices of the same degree

A: Solution: Suppose G is a finite simple graph with n vertices.  Since G is simple, no vertex is…

Q: 1. Prove that in a finite directed graph if every edge has at least one outgoing edge, then the…

A: 1. It is given that the graph is directed and finite.Therefore it has finite vertex and it is given…

Q: 2 3

A: For a vertex x, the pair a,b under consideration are such that  i) a≠x,b≠x and  ii) there is a…

Q: Prove that the graph below is non-planar.

A: Given the graph:           Prove that the graph is non-planar.

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: The graph of y+z² = 25 in 3-space

A: We will solve the following.

Q: Draw a complete graph so that it has symmetry with respect to the origin. (0,0) (x,0) -2t -2-

A: Topic = Graphs Correct option = C

Q: Two simple graphs are if there is a bijection from the vertices of the first graph to the vertices…

A: To fill the correct answer in the blank space.

Q: Give an example of two undirected graphs G1 with nodes {f, s, y, r} and G2 with nodes {t, q, n, p,…

A:

Q: A certain shade of purple paint is made by mixing blue and red paint. The relationship between the…

A: Given, number of quarts of Blue paint is represented by x  number of quarts of Red paint is…

Q: How many edges do the wheel Wn  and the complete tripartite graph Kr,s,t have?

A: The objective is to estimate the number of edges in a wheel Wn and complete tripartite graph Kr,s,t.

Q: Show that the Petersen graph is nonplanar. [Hint: show that the graph is edge contractible to Ks).

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

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

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Q: Give an example of a graph on 8 vertices which is i) Hamiltonian but not Eulerian. ii) Eulerian but…

A: A connected graph G is Hamiltonian if there is a cycle in G which covers every vertex of G exactly…

Q: Define the hypercube Qn as follows. The vertex set of Qn is the collection of all 01-strings of…

A: Qn is the hypercube graph whose vertices can be uniquely labeled by strings of zeros and ones of…

Q: Prove that if a plane graph G has n vertices, e edges, f faces and k components, then n−e+ f = k +1.

A: Euler’s Theorem: According to Euler's Theorem, V-E+F=2 Where, V is the number of vertices. E is the…