\(K_4\) does not have an Euler path or circuit.
\(K_5\) has an Euler circuit (so also an Euler path).
\(K_{5,7}\) does not have an Euler path or circuit.
\(K_{2,7}\) has an Euler path but not an Euler circuit.
\(C_7\) has an Euler circuit (it is a circuit graph!)
\(P_7\) has an Euler path but no Euler circuit.