3. Draw all the simple cubic graphs with at most 8 vertices.

Q: How many distinct unlabeled simple graphs on five nodes with equal to or less than five edges? 0 12…

A: The given question is related with graph theory. Here we have to find the number of distinct…

Q: 3. Find all connected sub-graphs of the following graph containing all of the vertices of the…

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Q: -3 -2 1. -2

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Q: er a 4-regular undirected graph that has 5 vertices. How many edges are ther

A: In this question, the number of edges is to be calculated when a 4-regular undirected graph has 5…

Q: Based on K1, K2, and K3, which graphs are not simple graphs? b a b. к, у K2 Y K3 Y K, and K2 a b K2…

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Q: 7. Is this the graph G planar? If so, then determine the faces and the edges.

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Q: Can a graph have 17 vertices where every vertex has either degree 1 or degree 3 or degree 5? Yes or…

A: Given  A graph with17 vertices  we have to prove that can a graph have 17 vertices where every…

Q: How many edges would a connected planar graph if it has 13 vertices and 9 faces?

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Q: Is it possible for a graph with 35 vertices and 100 edges to be planar? O Yes O No

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Q: Prove that there must be at least two vertices with the same degree in a simple graph

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Q: 3. а) Define the following terms as used in graph theory: i) regular graph ii) simple circuit

A: A graph is called a regular graph as graph it degree of each vertex. is equal. A graph is called k…

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

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Q: The number of even degree vertices in a simple graph must be even. O true O false

A: To state true or false given statement.

Q: Show that every graph with n vertices and k edges, n> k has n – k components.

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Q: How many different labelled graphs are there on the vertex set [n]? Justify your claim.

A: Given Vertex set n Let vertex V=1, 2, 3, ........., n Each graph G with a vertex V is determined by…

Q: When n = 3, there are nonisomorphic simple graphs.

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Q: In Problem ,draw a complete graph so that it has the type of symmetry indicated.

A: Given that, This is the graph is an upper horizontal half parabola whose vertex at -4, 0 crosse…

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: How many different simple graphs are there om the vertex set [n]?

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Q: (b) Give an example of a disconnected simple graph on n vertices in which every vertex has degree…

A: We need to give an example of a disconnected simple graph on n vertices in which every vertex has…

Q: 1.1 How many simple graphs are there of four vertices? Draw all of them.

A: As per our guidlines we are supposed to solve only one question that is the first problem. For the…

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

A: The level of a vertex v in a rooted tree is the length of the unique path from the root to this…

Q: 1. Determine and discuss which of the following graphs are connected or disconnected. a) 13 O 15 x6…

A: There is no such introduction for the solution.I have explained it within the solution.Please go…

Q: How can one prove a graph is connected?

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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: A. Find the number of vertices, the number of edges, and the degree of each vertex of the following…

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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: Determine the number of distinct unlabeled simple graphs (not necessarily connected) up to 4 nodes.…

A: To determine the number of distinct unlabelled simple graphs upto 4 nodes.

Q: . What is the order and size of the join of two graphs?

A: Given: To explain the given statement is given as,

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: Find the vertices and the area of the triangle formed by the graphs of y=|x-3| and -x+2y=5?

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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: This refers to the number of edges incident to a particular vertex. Answer:

A: Explanation of the answer is as follows

Q: is The number of edges in a complete bipartite graph K5 O 15 O 20 O 30 O 10

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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: What is the distance between the vertices of the graphs corresponding to y = 4(x - 2)2 + 1 and y =…

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Q: 5. Find the number of faces in the planar graph given below. d.

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Q: 10. Determine whether the given graphs are bipartite or not. а. b. b d

A: Graph theory, bipartite graph

Q: Are the following 2 graphs isomorphic? Discuss your answer with appropriate reasoning.

A: Given two graphs. From the first graph, d(u1)=3d(u2)=3d(u3)=2d(u4)=2d(u5)=3d(u6)=3

Q: for which values of m and n are km,n regular?

A: Given: A simple graph is called regular if every vertex of this graph has the same degree. A regular…

Q: 4. Draw the smallest hypercube graphs which is non plan

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Q: True or False: There exists a simple graph with 9 vertices each of degree 5. O True O False

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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: Prove that in any simple graph G with n vertices and m edges, 2m ≤ n^2 − n.

A: We need to prove that in any simple graph G with n vertices and m edges, 2m≤n2−n

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: How many possible graphs can be created on 5 distinct vertices?

A: Consider a graph of n vertices.The line connecting any two vertices of a graph is called as an edge…

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

A: Note - Acc. to Bartleby guidelines, we are supposed to do only first 3 subparts . If you want more…

Q: 1. Which of the graphs below are bipartite? Justify your answers.

A: We are entitled to solve only one ques at a time and up to 3 sub-parts only. To find - Which of the…

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

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