Prove the chromatic number of any tree is two. Recall, a tree is a connected graph with no cycles. (a) Describe a procedure to color the tree below. /attached picture/ (b) The chromatic number of Cn is two when n is even. What goes wrong when n is odd? (c) Prove that your procedure from part (a) always works for any tree.

Q: QUESTION 16 Suppose non – leaf nodes are 31, then depth of this complete binary tree is 30 32 5

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Q: 3. Find the tree and tree cover of Petersen graph. ***** *****

A: The Petersen Graph

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Q: Question 14 The following graph is a tree: O True O False 2 4 5 6

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Q: 4. Prove that the following is another drawing of the Petersen graph.

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Q: 9. Draw a graph or multigraph without loops with 8 vertices and at least 12 edges that has both an…

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Q: in a graph :is K-chromatic? give an examples

A: Please see the attachment

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Q: 1a. Prove: every tree with n ≥ 2 vertices has at least 2 leaves. (3 pt) 1b. Let T be a tree. Prove:…

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Q: 4.) Determine whether there is a graph with the given conditions. In each case, if such graph, or…

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

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A: Solution:-

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Q: What is the chromatic number of a full m-ary tree of height h? Select one: O a. 2 O b. 1 C. h O d. m…

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Q: 2) While out to dinner you have to choose an entrée, either seafood or pasta. You then have to…

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Q: tree

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Q: a) Is it possible to construct a simple graph with degree sequence 2, 2, 2, 2, 2, 3, 3, 3 Either…

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Q: The total degree of a tree with m vertices is (2m-2). True O False

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Q: 4. Use the Pruning Map Bijection outlined in Lecture 23 to do the following. (a) Find the word…

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Q: (c) Graph J is connected and has 74 vertices. If any of its edges is removed, the resulting subgraph…

A: Note: Tree: A connected graph without any cycles is called a tree.

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Q: A tree diagram has two stages. Stage 1 has three nodes and stage 2 has six nodes. In stage 1, the…

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Q: (d) Now, prove using induction that every tree has chromatic number 2.

A: We have to prove by induction that every tree has chromatic number 2

Q: Eulerize the following graph and identify one Euler circuit in your new graph

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Q: c) A 3-ary tree of height 3 with exactly 19 leaf vertices.

A: To construct a 3-ary tree of height 3 with exactly 19 leaf vertices, we can follow these steps:

Q: 2. A Tree is a connected O None of the above cyclic directed graph cyclic undirected graph O acyclic…

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Q: Draw a graph of [k 4].

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Q: What is the chromatic number of a tree with branching factor 4 and height 6? (That is, every…

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