Joel A. Christophel
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 Dec12 awarded Popular Question Dec8 comment How many nonisomorphic graphs are there with 10 vertices and 43 edges? Is my third attempt sound? Dec8 revised How many nonisomorphic graphs are there with 10 vertices and 43 edges? added 318 characters in body Dec8 comment How many nonisomorphic graphs are there with 10 vertices and 43 edges? So, as clarification, the graphs in bullet point one would still count as one non-isomorphic graph, correct? I've made some revisions to my solution. Dec8 revised How many nonisomorphic graphs are there with 10 vertices and 43 edges? added 318 characters in body Dec8 comment How many nonisomorphic graphs are there with 10 vertices and 43 edges? One thing that's tripping me up is that I'm not sure what it means for one graph to be isomorphic. It's usually in the context of two graphs. Is it asking for the number of "non-isomorphic classes"? Dec8 comment How many nonisomorphic graphs are there with 10 vertices and 43 edges? I think I like this framing better. Dec8 comment How many nonisomorphic graphs are there with 10 vertices and 43 edges? Would you mind explaining why the former are all isomorphic but not all of the latter are? Dec8 suggested rejected edit on Graph Theory - How can I calculate the number of vertices and edges, if given this example Dec8 asked How many nonisomorphic graphs are there with 10 vertices and 43 edges? Dec8 comment Proper $n$-coloring of a graph clarification There are theorems for 4, 5 and 6 colors. Dec8 accepted Proper $n$-coloring of a graph clarification Dec8 asked Proper $n$-coloring of a graph clarification Dec5 accepted Prove chromatic polynomial of n-cycle Dec5 comment Prove chromatic polynomial of n-cycle Okay, that makes sense. What happens on the second to last line of the proof? Dec5 comment Prove chromatic polynomial of n-cycle What are $C_1$ and $C_2$? Dec5 asked Prove chromatic polynomial of n-cycle Nov21 awarded Yearling Nov21 comment Counting 5-letter words that include at least one vowel While some of the other answers were very helpful, this solution most clearly demonstrates how the overcounting happens with the erroneous solution. Nov21 accepted Counting 5-letter words that include at least one vowel