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

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

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?

2. ## 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.