Problem-82

Problem-82

The intersection graph of a collection of sets A1, A2, . . . , An is the graph that has a vertex for each of these sets and has an edge connecting the vertices representing two sets if these sets have a nonempty intersection. Select the intersection graph of these collections of sets.

a)
A1={0, 2, 4, 6, 8}, A2={0, 1, 2, 3, 4},
A3={1, 3, 5, 7, 9}, A4={0, 1, 8, 9},
A5={5, 6, 7, 8, 9}.

b)
A1={. . . ,−6,−3, 0, 3, 6, . . .}, A2={. . . ,−4,−3,−2,−1, 0},
A3={. . . ,−2,−1, 0, 1, 2, . . .}, A4={. . . ,−6,−4,−2, 0, 2, 4, 6, . . .},
A5={. . . ,−5,−3,−1, 1, 3, 5, . . .}.

c)
A1={x|0<x<1}, A2={x|−1<x<1},
A3={x|x>−1}, A4=R,
A5={x|x<0}, A6={x|−1<x<0}.

 

Solution

a)

intersection graph 1

b)

intersection graph 2

c)

intersection graph 3

 

One Response to “Problem-82”

  • Thomas says:

    I was wondering if you knew where to find a program, hopefully free, that would allow me to construct graphs out of directions like this problem has. Thanks

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