Networks in Geometry
Math ⇒ Geometry
Networks in Geometry starts at 9 and continues till grade 12.
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See sample questions for grade 10
A network has 10 vertices and 15 edges. If it is connected and has no cycles, what type of network is it?
A network has 12 vertices and 11 edges. If it is connected, what type of network is it?
A network has 5 vertices and 4 edges. If it is connected, what type of network is it?
A network has 5 vertices and 7 edges. How many edges must be removed to make it a tree?
A network has 10 vertices and 15 edges. If it is connected and has no cycles, what type of network is it?
A network has 12 vertices and 11 edges. If it is connected, what type of network is it?
A network has 5 vertices and 4 edges. If it is connected, what type of network is it?
A network has 5 vertices and 7 edges. How many edges must be removed to make it a tree?
Which of the following is a necessary condition for a network to have a Hamiltonian cycle? (1) All vertices have even degree. (2) The network is connected. (3) The network is planar. (4) The network is a tree.
Which of the following is a necessary condition for a network to have an Eulerian circuit? (1) All vertices have even degree. (2) All vertices have odd degree. (3) The network is disconnected. (4) The network has no cycles.
Which of the following is a property of a planar network? (1) It can be drawn without any edges crossing. (2) It must be a tree. (3) It has only even degree vertices. (4) It is always complete.
Which of the following is NOT a necessary condition for a network to be connected? (1) There is a path between every pair of vertices. (2) The network has no isolated vertices. (3) The network has at least one cycle. (4) The network has at least (n-1) edges, where n is the number of vertices.
Fill in the blank: A network in which every pair of vertices is connected by exactly one path is called a __________.
Fill in the blank: A network with no cycles is called a __________ network.
Fill in the blank: In a network, a vertex of degree 1 is called a __________.
Fill in the blank: The degree of a vertex in a network is the number of __________ connected to it.
A network has 7 vertices and 7 edges. Can it be a tree?
A network has 8 vertices and 12 edges. Is it possible for this network to be a tree?
True or False: A network with a Hamiltonian cycle must also have an Eulerian circuit.
True or False: A planar network can be drawn on a plane without any edges crossing.
