A route network has roads A–B,B–C and D–E, with no other roads. Can a traveller reach E from A?
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Answer: No: they lie in different connected components
A,B and C form one component; D and E form another. No edge links these components.
Example 2
A star-shaped network has one central vertex joined to 11 distinct outer vertices. No other edges touch the centre. What is the degree of the central vertex?
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Answer: 11
The degree counts incident edges: 11 edges touch the centre.
Example 3
Route A–B–D uses roads of lengths 5km and 3km. Route A–C–D uses roads of lengths 3km and 5km. Find the shorter route length, in km.
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Answer: 8
The totals are 8km and 8km. Choose the smaller, 8km.
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