Graphical degree sequences

#degree sequence#graphical#Erdős–Gallai

Statement

Is $(3,3,3,1,1)$ a graphical degree sequence?

Hint

Erdős–Gallai or handshake check: sum of degrees must be even.

Show solutionHide solution

Handshake check. $3+3+3+1+1=11$ , odd. So $(3,3,3,1,1)$ cannot be the degree sequence of any graph.

Conclusion. Not graphical (sum is odd).