Networks in Geometry
Math ⇒ Geometry
Networks in Geometry starts at 9 and continues till grade 12.
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Describe the difference between a path and a cycle in a network.
Describe the process of finding the shortest path in a weighted network.
Describe what is meant by a weighted network.
Explain the difference between a directed and an undirected network.
Explain the difference between a tree and a cycle in a network.
Explain the significance of Euler's formula in planar networks.
Explain what is meant by a planar network.
Explain why a network with all vertices of odd degree cannot have an Eulerian circuit.
Which formula relates the number of vertices (V), edges (E), and regions (F) in a connected planar network? (1) V + E = F + 2, (2) V - E + F = 2, (3) V + F = E + 2, (4) V - F + E = 2
Which of the following is a necessary condition for a network to be connected? (1) There is a path between every pair of vertices, (2) All vertices have even degree, (3) The network has no cycles, (4) The network is planar
Which of the following is a necessary condition for a network to have an Eulerian trail? (1) All vertices have even degree, (2) Exactly two vertices have odd degree, (3) All vertices have odd degree, (4) No vertex has degree zero
Which of the following is a property of a Hamiltonian cycle? (1) It visits every edge exactly once, (2) It visits every vertex exactly once, (3) It is only possible in trees, (4) It requires all vertices to have even degree
Fill in the blank: A network in which every pair of vertices is connected by an edge is called a ________ network.
Fill in the blank: A network with no cycles is called a ________.
Fill in the blank: In a network, a vertex with degree zero is called an ________ vertex.
Fill in the blank: The degree of a vertex in a network is the number of ________ incident to it.
A network has 5 vertices and 7 edges. Is it possible for this network to be a tree?
True or False: A Hamiltonian path visits every edge of a network exactly once.
True or False: A network with 2 vertices and 1 edge is a tree.
True or False: A network with 5 vertices and 4 edges can be a tree.
