True or False? A pseudograph differs from a multi graph by containing loops, an

Question

True or False? A pseudograph differs from a multi graph by containing loops, an edge from a vertex to itself. True False In a niche overlap graph, which of the following pairs of species would be connected by an edge? leeches and vampires squirrels and hawks hawks and falcons eagles and deer What type of a path or circuit does a multigraph have if the degrees of vertices are 2, 3, 4, 3, and 2? Euler circuit Euler path Hamilton circuit Hamilton path Choose which of the following bipartite graphs with an odd number of vertices have a Hamilton circuit. Town marriage graph Relation between two sets Set of legal checker moves none The Math Department has 6 committees that meet once a month. How many different meeting times must be used to guarantee that no one is scheduled to be at 2 meetings at the same time, if committees and their members are: Cl = {Allen, Brooks, Marg}, C2 = {Brooks, Jones, Morton}, C3 = {Allen, Marg, Morton}, C4 = {Jones, Marg, Morton}, C5 = {Allen, Brooks}, C6 = {Brooks, Marg, Morton}? 6 5 4 3 True or False? All connected multi graphs have Euler circuits. True False True or False? The shortest path between two vertices in a weighted graph is unique if the weights of edges are unique (all different). True False 8. True or False? Five houses can be connected to two utilities without the connections crossing. True False A connected planar graph has 8 vertices, each of degree 3. Into how many regions is the plane divided by a planar representation of this graph? 4 5 6 7 A connected planar graph has 30 edges. If a planar representation of this graph divides the plane into 20 regions, how many vertices does the graph have? 10 11 12 13

Explanation / Answer

1. a true

2. c hawks and falcons

3. c hamilton circuit

4. b relation between two sets

5. c 4

6. a true

7. a true

8. b false

9. a 4

10. a 10

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