A forest contains 23 vertices and 20 edges. How many connected components does the graph have?
Let G be a connected graph with n vertices and n edges. How many cycles does G have? Explain your answer.
how many edges does a 4-regular graph on n on vertices have?
1) Suppose that a directed graph contains the following edges. Find the strongly connected components. {(h, i), (i, j), (j, k), (k, h), (l, m), (m, n), (n, p), (p, l), (f, i), (c, e), (j, b), (k, l), (a, b), (b, c), (c, a), (d, e), (e, f), (f, g), (g, d)}. a) How many vertices are there in the component having the smallest number of vertices? b) How many vertices are there in the component having the second...
Problem 1: In the graph below 6 5 4 1 3 (a) How many edges does the graph have? (b) Which vertices are odd, and which vertices are even? (c) is the graph connected? (d) Does the graph have any bridges? If so, list them all.
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?
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?
(7) Sketch any connected 3-regular Graph G with 6 vertices, determine how many edges must be removed to produce a Spanning Tree and then sketch any Spanning Tree.
Recall the definition of the degree of a vertex in a graph. a) Suppose a graph has 7 vertices, each of degree 2 or 3. Is the graph necessarily connected ? b) Now the graph has 7 vertices, each degree 3 or 4. Is it necessarily connected? My professor gave an example in class. He said triangle and a square are graph which are not connected yet each vertex has degree 2. (Paul Zeitz, The Art and Craft of Problem...
Problem 2. Let G be connected graph with 12 vertices. Suppose that it admits an planar embedding G C R2 dividing the plane R2 into 20 faces. How many edges does G have?
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