# Connected graphs on $m$ vertices and $n$ edges

What's number of connected graphs on $m$ vertices (unlabeled) and $n$ edges ? For example $m = 5$ and $n = 5$ , the answer is $5$ . When the $m$ and $n$ become greater , it's not possible to draw all graphs . I'm curious about the general formula .

• Have a look at this sequence. – Jens Sep 10 '17 at 12:37
• @Jens Thanks , can you explain that because I'm not familiar with OEIS ? – S.H.W Sep 10 '17 at 13:17
• Look at the example in the link. First row is for $n=1$, $k=0$. Second row is for $n=2$, $k=0, 1$. Third row is for $n=3$, $k=0, 1, 2, 3$. You can find your own example in the fifth row, where for $k=5$ the answer is $5$. – Jens Sep 10 '17 at 13:28
• you may find an answer in [How many connected graphs V vertices and E edges] – Shubhrajit Bhattacharya Sep 10 '17 at 14:06
• This problem was also discussed at the following MSE link. – Marko Riedel Sep 10 '17 at 23:13