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Math Help - Construct graph with virtices

  1. #1
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    Construct graph with virtices

    Hi,

    Please help me to solve this problem?


    1. Is it possible to construct a simple graph with the following condition, if not why?

    a. Graph on 7 vertices having degree 5,3,3,2,2,1,0
    b. 3-regular graph on 6 vertices
    c. 4-regular graph on 6 vertices
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  2. #2
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    Re: Construct graph with virtices

    a) Take a pentagon, put a 6th vertex in the middle. Connect the middle vertex to all vertices of the pentagon. Pick a vertex on the pentagon. Remove the two edges adjacent to this vertex and on the pentagon (i.e., not towards the middle vertex). Add a 7th vertex without any edges. This is your graph.

    b) It is often easier to create the complementary graph. So, try creating a 2-regular graph on 6 vertices (there are 2 such graphs, up to isomorphism).

    c) try the same trick as in b)
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  3. #3
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    Re: Construct graph with virtices

    Thanks a lot.
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