Problem
COM-B1-M09-P002 Three Odd Degrees
#2
★☆☆☆☆ Level 1 of 5
Can there exist a graph with three vertices of degrees \(1,1,1\)?
The degree sum must be even.
The degree sum is \(3\), which is odd. But the degree sum of any graph is \(2E\), hence even. Such a graph does not exist.
Minimal impossibility example.