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set & relation, function, tree, graph - Coggle Diagram
set & relation
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A reflexive relation A R A, ex: =, <=
A symmetric relation A R B & B R A, eg: =,
A transitive relation A R B, B R C => A R C, eg: <, <=, =
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function
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f1 = f2: domain, codomain, f1(a) = f2(a) for all domain elements
a sequence of length N is an actual function of domain [0,1, ... , N-1]
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f(a) -> a is a value
f(A) -> A is a set, f(A) is an image of domain A
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tree
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acyclic & connected graph
acyclic -> |V| = |E| + 1
acyclic + connected -> single path between any two vertices
ordered tree vs positional tree
ordered -> relative position around children
positional -> fixed position around children
Properties:
- single path between any two nodes
- |E| = |V| - 1
- tree becomes disconnected if removing any edge
- tree is connected and acyclic
- adding any edge will lead to a cycle
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