  In order to unravel the composition of the isoscalar $DN$, $D^*N$, $D_1N$,
and $D_2^*N$ molecular pentaquarks, we carry out a systematic investigation of
their M1 radiative decays and magnetic moment properties. Using the constituent
quark model and taking into account the $S$-$D$ wave mixing effect and the
coupled channel effect, our analysis yields numerical results indicating that
the M1 radiative decays and the magnetic moment properties of these molecular
pentaquarks provide some insights into their inner structures. These results
can serve as crucial clues for distinguishing their spin-parity quantum numbers
and configurations in experimental studies. In addition, we highlight the
importance of the electromagnetic properties as key observables for elucidating
the inner structures of the observed $\Lambda_c^{+} (2940)$ and $\Lambda_c^{+}
(2910)$. We hope that these discoveries will inspire our experimental
colleagues to further explore the family of the single-charm molecular
pentaquarks and to investigate the inner structures of the $\Lambda_c^{+}
(2940)$ and $\Lambda_c^{+} (2910)$ in future studies.
