As per Handshaking Lemma, I suspect such graph cannot be formed (because even no. of vertex is having even degree and not odd : vertex 6 has degree 2). But I am able to draw a graph. Does such graphs exists?
2026-05-05 00:05:09.1777939509
Prove if 5;5;3;3;2;2;2 forms a graphical sequence.
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The fact that you can draw a graph with that degree sequence proves that the sequence is graphical. What makes you think it's not? The Handshaking Lemma says that the sum of the degrees is an even number, equal to twice the number of edges. Sure enough, $5+5+3+3+2+2+2=22$ is an even number, so everything is fine. I guess the graph you drew has $11$ edges?