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The London penetration depth, $lambda (T)$ was measured in single crystals of Ce$_{1-x}R_x$CoIn$_5$, $R$=La, Nd and Yb down to 50~mK ($T_c/T sim$50) using a tunnel-diode resonator. In the cleanest samples $Delta lambda (T)$ is best described by the p ower law, $Delta lambda (T) propto T^{n}$, with $n sim 1$, consistent with line nodes. Substitutions of Ce with La, Nd and Yb lead to similar monotonic suppressions of $T_c$, however the effects on $Delta lambda(T)$ differ. While La and Nd doping results in an increase of the exponent to $n sim 2$, as expected for a dirty nodal superconductor, Yb doping leads to $n > 3$, inconsistent with nodes, suggesting a change from nodal to nodeless superconductivity where Fermi surface topology changes were reported, implying that the nodal structure and Fermi surface topology are closely linked.
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