Bonsoir friend, we’ll quickly be discussing the difference between maximal, minimal, maximum, and minimum concepts applying them to graph theory.
Maximal
We can define Maximal in Graph Theory as:
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Let F’ be a set of subgraphs from G, a member F of F’ is maximal if no other member of F’ has F as a subgraph.
(In other words, F is not contained by any graph in F’)
(in other words, F is the biggest subgraph of F’)
Minimal
Therefore, we can define Minimal in Graph Theory like:
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Let F’ be a set of subgraphs from G, a member F of F’ is minimal if it has no member of F’ as a subgraph.
(In other words, F does not contain any other subgraph in F’)
(in other words, F is the smallest subgraph of F’)
Maximum
Let X be a subset of set A.
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We could say X is maximum if there’s no other subset Y in A such it has bigger cardinality than X.
*(In other words, X is maximum if there is no other Y ∈ A such Y > X .)* Proposition: Every Maximum is Maximal, but not every Minimum is Minimal.
Minimum
Let X be a subset of set A.
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We could say X is minimum if there’s no other subset Y in A such it has smaller cardinality than X.
(In other words, X is minimum *if there is no other Y ∈ A such Y < X .)*