Draw a graph with 5 vertices, ten edges and no cycles
Discrete Mathematics
6: A: Draw a graph with 5 vertices and the requisite number of edges to show that if four of the vertices have degree 2, it would be impossible for the 5 vertex to have degree 1. Repetition of edges is not permitted. (There may not be two different bridges connecting the same pair of vertices.) B: Draw a graph with 4 vertices and determine the largest number of edges the graph can have, assuming repetition of edges...
Let G be a connected graph with n vertices and n edges. How many cycles does G have? Explain your answer.
2. If possible, draw a simple graph with 11 edges and all vertices are of degree 3. If no such graph exists, explain why.
6. (4pts) Draw a simple graph with nine edges and all vertices of degree 3. (this is possible)
A graph has 21 edges, two vertices of degree 5, four vertices of degree 3, and all remaining vertices have degree 2. How many vertices does the graph have? 12 10 16 O 14
Prove that any graph with n vertices and at least n + k edges must have at least k + 1 cycles.
Most Edges. Prove that if a graph with n vertices has chromatic number n, then the graph has n(n-1) edges. Divide. Let V = {1, 2, ..., 10} and E = {(x, y) : x, y € V, x + y, , and a divides y}. Draw the directed graph with vertices V and directed edges E.
Draw a picture of the graph with vertices {v1, v2, v3} and edges {(v1, v1), (v1, v2), (v2, v3), (v2, v1), (v3, v1)}. (2 Points)
2 (a) Draw the graphs K5,2 and K5,3 using the standard
arrangement.
For example, K5,2 should have a row of 5 vertices above a row of
2 vertices, and the edges connect each vertex in the top row to
each vertex in the bottom row.
(b) Draw K5,2 as a plane graph, i.e., with no edges
crossing.
(c) Complete the following table, recalling E is the number of
edges in a graph and V is the number of vertices. (Strictly...
Draw a simple undirected graph G that has 12 vertices, 18 edges, and 3 connected components. Why would it be impossible to draw G with 3 connected components if G has 66 edges?