Isomorphism Classes for Order 2 Simple Graphs

Theorem

There are $2$ equivalence classes for simple graphs of order $2$ under graph isomorphism:

the edgeless graph of order $2$

and

the complete graph of order $2$.

Proof

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Sources

• 1977: Gary Chartrand: Introductory Graph Theory ... (previous) ... (next): Chapter $2$: Elementary Concepts of Graph Theory: $\S 2.2$: Isomorphic Graphs