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Consider this map of the New Zealand North Island showing each of the regions in a different colour. (a) (4 marks) Draw...
Draw a planar graph(with no loops or multiple edges) for each of the following properties, if...
Draw a planar graph(with no loops or multiple edges) for each of the following properties, if possible. If not possible, explain briefly why not. b) 8 vertices, all of degree 3 ( how many edges and regions must there be) c) has exactly 7 vertices, has an euler cycle and 3 is minimum vertex coloring number Also please draw the graph.
11. The twenty-two regions of France are shown on this map. MOROS BASSE LORRAIN PONTOU CHARENTES...
11. The twenty-two regions of France are shown on this map. MOROS BASSE LORRAIN PONTOU CHARENTES COTE DA (a) When this map is turned into a graph, how many edges will be at the vertex CENTER? (b) When this map is turned into a graph, would the graph be planar or non-planar? (c) When this map is turned into a graph, how many edges would be at the vertex ILE-DE-FRANCE? (d) When this map is turned into a graph. could...
North Bank South Bank How many vertices are in your graph? How many edges are in...
North Bank South Bank How many vertices are in your graph? How many edges are in your graph? Give the degree of each vertex: deg(A) = , deg(B) = , deg(C) = , deg(North) = deg(South) = Does this graph have an Euler Circuit, an Euler Path, or Neither?
8. For each of the following, either draw a undirected graph satisfying the given criteria or explain why it cannot be done. Your graphs should be simple, i.e. not having any multiple edges (more tha...
8. For each of the following, either draw a undirected graph satisfying the given criteria or explain why it cannot be done. Your graphs should be simple, i.e. not having any multiple edges (more than one edge between the same pair of vertices) or self-loops (edges with both ends at the same vertex). [10 points] a. A graph with 3 connected components, 11 vertices, and 10 edges. b. A graph with 4 connected components, 10 vertices, and 30 edges. c....
8. For each of the following, either draw a undirected graph satisfying the given criteria or...
8. For each of the following, either draw a undirected graph satisfying the given criteria or explain why it cannot be done. Your graphs should be simple, i.e. not having any multiple edges (more than one edge between the same pair of vertices) or self-loops (edges with both ends at the same vertex). [10 points] a. A graph with 3 connected components, 11 vertices, and 10 edges. b. A graph with 4 connected components, 10 vertices, and 30 edges. c....
Please answer only problem 2. Accurate answers with work shown will receive a 100% rating ASAP....
Please answer only problem 2. Accurate answers with work shown
will receive a 100% rating ASAP. Thank you!
Let G = (V, E) be a graph. We say that a subset S of the vertices V is an independent set if there is no edge in G joining two vertices in S. For example, given a proper colouring of the vertices of G, each colour class (i.e. the set of vertices that have some fixed colour) forms an independent set,...
Bonus 1 A walk in a graph G is a sequence of vertices V1, V2, ...,...
Bonus 1 A walk in a graph G is a sequence of vertices V1, V2, ..., Uk such that {Vi, Vi+1} is an edge of G. Informally, a walk is a sequence of vertices where each step is taken along an edge. Note that a walk may visit the same vertex more than once. A closed walk is a walk where the first and last vertex are equal, i.e. v1 = Uk. The length of a walk is the number...
Answer each question in the space provided below. 1. Draw all non-isomorphic free trees with five...
Answer each question in the space provided below. 1. Draw all non-isomorphic free trees with five vertices. You should not include two trees that are isomorphic. 2. If a tree has n vertices, what is the maximum possible number of leaves? (Your answer should be an expression depending on the variable n. 3. Find a graph with the given set of properties or explain why no such graph can exist. The graphs do not need to be trees unless explicitly...
11. The twenty-two regions of France are shown on this map. MOROS BASSE LORRAIN PONTOU CHARENTES COTE DA (a) When this map is turned into a graph, how many edges will be at the vertex CENTER? (b) When this map is turned into a graph, would the graph be planar or non-planar? (c) When this map is turned into a graph, how many edges would be at the vertex ILE-DE-FRANCE? (d) When this map is turned into a graph. could...
North Bank South Bank How many vertices are in your graph? How many edges are in your graph? Give the degree of each vertex: deg(A) = , deg(B) = , deg(C) = , deg(North) = deg(South) = Does this graph have an Euler Circuit, an Euler Path, or Neither?
8. For each of the following, either draw a undirected graph satisfying the given criteria or explain why it cannot be done. Your graphs should be simple, i.e. not having any multiple edges (more than one edge between the same pair of vertices) or self-loops (edges with both ends at the same vertex). [10 points] a. A graph with 3 connected components, 11 vertices, and 10 edges. b. A graph with 4 connected components, 10 vertices, and 30 edges. c....
8. For each of the following, either draw a undirected graph satisfying the given criteria or explain why it cannot be done. Your graphs should be simple, i.e. not having any multiple edges (more than one edge between the same pair of vertices) or self-loops (edges with both ends at the same vertex). [10 points] a. A graph with 3 connected components, 11 vertices, and 10 edges. b. A graph with 4 connected components, 10 vertices, and 30 edges. c....
Please answer only problem 2. Accurate answers with work shown
will receive a 100% rating ASAP. Thank you!
Let G = (V, E) be a graph. We say that a subset S of the vertices V is an independent set if there is no edge in G joining two vertices in S. For example, given a proper colouring of the vertices of G, each colour class (i.e. the set of vertices that have some fixed colour) forms an independent set,...
Bonus 1 A walk in a graph G is a sequence of vertices V1, V2, ..., Uk such that {Vi, Vi+1} is an edge of G. Informally, a walk is a sequence of vertices where each step is taken along an edge. Note that a walk may visit the same vertex more than once. A closed walk is a walk where the first and last vertex are equal, i.e. v1 = Uk. The length of a walk is the number...
Answer each question in the space provided below. 1. Draw all non-isomorphic free trees with five vertices. You should not include two trees that are isomorphic. 2. If a tree has n vertices, what is the maximum possible number of leaves? (Your answer should be an expression depending on the variable n. 3. Find a graph with the given set of properties or explain why no such graph can exist. The graphs do not need to be trees unless explicitly...
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