Show that the graph is 2-colorable by finding a 2-coloring. If the graph is not 2-colorable, explain why. Blue Red Green Green Blue Green Red Green Green Red] Blue Red Blue Red Green Green Red Green Green) Green Green (Green) Blue Red The graph is not two-colorable because it has a circuit that consists of an odd number of vertices.

Q: 1. Is there a connected graph whose degree are: a. 5, 3, 2, 2, 2, 1, 1

A: As per bartleby guidelines for more than one questions asked only first should be answered. Please…

Q: The graph G is a planar connected graph. It has 23 edges, and 8 faces. How many vertices does G…

A: I have given the answer in the next step. Hope you understand that

Q: in a graph What is the vertex coloring? And give an examples

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Q: Consider the following graph: Provide a topological ordering of the vertices in this graph if there…

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Q: . Consider a connected graph on 100 vertices with 99 edges. What's the mallest number of colors you…

A: If there is a connected graph with n vertex and n-1 edges then graph must be a path P(n).  Every…

Q: this graph connected? O Connected ONot Connected

A: Note that the graph is said to be connected if the pair of any two vertices is connected by a path.

Q: Construct a graph that is a tree with vertices P, Q, R, S,T,U,V such that the degree of Q is 6. What…

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Q: 3. Determine the edge connectivity and the vertex connectivity of the following graph. Explain.

A: The vertex connectivity is the minimum number of vertex required to remove from graph to make graph…

Q: number

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Q: pns called digraphs. By determining which vertices should be red, green, and blue, give a proper…

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Q: For the graph shown below, find a 2-coloring of the vertices or explain why a 2-coloring is…

A: Let us name the vertices in the given graph: A 2-coloring graph means we can color the vertices of…

Q: 12. A department wants to schedule final exams so that no student has more than one exam on any…

A: According to the given information it is required to fin da way to color the vertices of graph using…

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: 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: Show that if a simple graph G ha

A: To prove that if a simple graph G has n vertices and at least n edges, then G must contain a cycle.

Q: In which of the following graph can red or blue be assigned to the vertices such that no two…

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Q: What is the minimum number of colors required to color each vertex the graph below so that no two…

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Q: The graph G is a planar connected graph. It has 22 edges, and 15 vertices. How many faces does G…

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Q: How can I prove "A graph is k-colourable if and only if it is k-partite.”?

A: As per the question we have to prove that a graph is k-colourable if and only if it is k-partite. To…

Q: Could there be a graph with four vertices of degree 1,2,5 and 4? Explain why no such graph exists or…

A: To verify whether a graph with 4 vertices of degree 1,2,5 and 4 exist or not.

Q: what is the edge - connectivity in a graph ? And give an example

A: Edge - Connectivity in a graph : Let ‘G’ be a given connected graph.Then the minimum number of edges…

Q: J A coloring of a graph is an assignment of colors (or labels) to the vertices of the graph such…

A: Given- A coloring of a graph is an assignment of colors (or labels) to the vertices of the graph…

Q: Prove or disprove: the following graph is 2-colorable.

A: In graph theory, a graph is said to be 2-colorable (or bipartite) if its vertices can be divided…

Q: A simple connected graph with 2,024 vertices is such that there are exactly two vertices, u and v,…

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Q: (a) Color the graph below. That is, using the smallest number of colors possible, color the vertices…

A: Now we have the given graph First, we will start at A, and fill it with the first color violet. Then…

Q: Given a graph B whose vertices have degree at most 3, show that you need at least 4 colors to color…

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Q: For the graph shown below, find a 2-coloring of the vertices or explain why a 2-coloring is…

A: Given:

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: 18. Color the vertices of the following graph so that no vertices of the same color share an edge.…

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Q: The graph G is a planar connected graph. It has 26 edges, and 19 vertices. How many faces does G…

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Q: What is the smallest number of colors you need to properly color the vertices of K4,5? That is, find…

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Q: How many edges does a complete graph K„ have? Prove / explain your answer.

A: The complete graph Kn is a graph with n vertices such that every there is exactly one edge between…