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...
how many edges does a 4-regular graph on n on vertices have?
A forest contains 23 vertices and 20 edges. How many connected components does the graph have?
(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.
Let G be a connected graph with n vertices and n edges. How many cycles does G have? Explain your answer.
A graph has 4 vertices of degrees 3, 3, 4, 4. (a) How many edges such a graph have? (b) Draw two non isomorphic such graphs. (c) Explain why there is no such simple graph
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
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....
a. b. c. d. e. What are the vertices? Is this graph connected? What is the degree of vertex C? Edge FE is adjacent to which edges? Does this graph have any bridges? Answer the following questions based on the graph below. 1w a. b. c. d. What are the vertices? What is the degree of vertex u? What is the degree of vertex s? What is one circuit in the graph?
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 stated. (a) tree, 7 vertices, total degree = 12. (b) connected, no multi-edges, 5 vertices, 11 edges. (c) tree, all vertices have degree <3, 6 leaves, 4 internal vertices. (d) connected, five vertices, all vertices have degree 3.