Let Degree sequence of a graph G is 5, 2, 2, 2, 2, 1. - Is S graphic? - How many edges does Graph G have? - Draw such a graph.
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Let Degree sequence of a graph G is 5, 2, 2, 2, 2, 1.
- Is S graphic?
- How many edges does Graph G have?
- Draw such a graph.
Step by step
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- If G is a graph with degree sequence(5,5,3,3,2,2,2), the how many vertices and how many edges does G have?Consider a graph on 4 vertices in the shape of a square. What is the degree sequence of the graph? How many faces does the graph have?For each candidate degree sequence below, either draw a graph with that degree sequence or explain why that list cannot be the degree sequence of a graph. (a) 4, 4, 4, 4, 4 (b) 6, 4, 4, 4, 4 (c) 0, 0, 0, 0, 0 (d) 3, 2, 1, 1, 1 (e) 3, 3, 2, 2, 1
- Determine whether the sequences are a degree sequence of a simple graph on five vertices. If it is true then show an example of a graph with the given degree sequence. If it is false, give a proof that it is not possible. (i) (3, 3, 3, 3, 2) (ii) (4, 4, 4, 2, 2) (iii) (2, 2, 1, 1, 1)it is Algorthms and graphs Theory question.(2.8 (ii)) Draw a graph on six vertices with degree sequence (2, 3,3,4,5, 5) does there exist a simple graph with these degreeWhich of the following degree sequences are possible for a simple graph?A. (1,3,2,3,2)B. (4,5,5,8,8,6,7,6,6,5)C. (5,7,7,7,6,7,6,8,7)D. (6,1,4,2,3,2)
- Let G be a simple, connected graph on n vertices (n≥3) Suppose that G has at least one cycle as a subgraph, what is the min number of edges G can have, in terms if n, please give an explanationA graph has a degree sequence 2,2,3,3,3,3,5. Find the number of edges of this graph and draw the graph.A city is built on the banks of a river and some islands in the river. The map below shows the bridges connecting the various land masses. Draw a graph that models the connecting relationships in the map below. The vertices represent the land masses and the edges represent bridges connecting them. Island CC is little more than a sandbar and is uninhabited. Is it possible to find a circuit through the city that uses each bridge once? If so, enter the sequence of land masses(vertices) visited, for example ABDEA. If it is not possible, enter DNE. image attached
- Is there a degree sequence such that the graph can only be drawn as a simple graph but not a multigraph? WhyLet H be the graph below: (a) How many trees, with vertex set [7], have H as a subgraph? (b) How many graphs, with vertex set [n] and n > 7, have H as a subgraph? (c) How many graphs, with vertex set [n] and n > 7, have H as an induced subgraph? (d) How many trees, with vertex set [n] and n > 7, have H as a subgraph? Hint: Moon’s theorem (e) How many trees, with vertex set [n] and n > 7, have H as an induced subgraph?a. Draw all non-isomorphic graphs with 3 edges on 6 vertices.b. Draw all non-isomorphic graphs with 4 edges on 5 vertices.c. Draw all connected non-isomorphic graphs with degree sequence 5,5,2,2,2,2,2,2,2,2.d. Draw all non-isomorphic trees with degree sequence 3,3,2,2,2,1,1,1,1.