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Math Help - Help Identifying the 3 Possible Cliques on this 4 Edge Simple Graph for me?

  1. #1
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    Help Identifying the 3 Possible Cliques on this 4 Edge Simple Graph for me?

    Help Identifying the 3 Possible Cliques on this 4 Edge Simple Graph for me?-math-qq.png

    I am having trouble understanding how to identify clique numbers in graphs. I easily understood how to find chromatic numbers, but I haven't cliques.

    Can anyone tell me via the variables ABCD the 3 possible clique combinations? And maybe give a simple explanation why?
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  2. #2
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    Re: Help Identifying the 3 Possible Cliques on this 4 Edge Simple Graph for me?

    I think I figured it out.

    The clique number is the maximum amount of vertices that are all adjacent to one another.

    ABD = three vertices all adjacent to one another.
    ACD = three vertices all adjacent to one another.

    Since the maximum amount of vertices adjacent to one another is 3. The clique number is 3.

    ABCD is not a clique because BC aren't adjacent. Also if the edge between A nd D did not exist the click number would be 2 because AB BD CD AC would be the maximum amount of vertices adjacent to one anohter.

    I hope this helps someone some day having trouble figuring this out.
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