Wykres relacji

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Graph of the relation Definition A directed graph is a set of points, together with a set of directed arcs connecting some of these points. The points of a directed graph are called vertices (singular: ver- tix) or the nodes of the graph. If D is a directed graph, then ν ( D ) is the set of vertices of D . The directions of arc in directed graph are denoted by arrows. The arcs in directed graph are described by ordered pairs of vertices. An arc from some vertex to itself is called a loop . Directed graphs are closely connected with binary relations - arcs of a directed graph D define a binary relation R on the vertices set ν ( D ) : ∀ u, v ∈ ν ( D ) u R v ⇔ ( u, v ) is an arc in D . For example: Graph in the picture defines the relation: R = { ( v 1 , v 2 ) , ( v 2 , v 3 ) , ( v 3 , v 1 ) , ( v 4 , v 2 ) , ( v 4 , v 3 ) , ( v 4 , v 4 ) } . Every binary relation R on a finite set A can be represented by a directed graph D - the elements of A are vertices of D and ( u, v ) is an arc in D ⇔ u R v . Such directed graph D is called the graph of the relation R . ... zobacz całą notatkę

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