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Zinc to cadmium cation exchange of ZnSe quantum dots has been used to produce a series of alloyed Zn_1-xCd_xSe quantum dots. As x increases and the lowest-energy exciton shifts to the red, the peak initially broadens and then sharpens as x approaches 1. Resonance Raman spectra obtained with excitation near the lowest excitonic absorption peak show a gradual shift of the longitudinal optical phonon peak from 251 cm^-1 in pure ZnSe to 210 cm^-1 in nearly pure CdSe with strong broadening at intermediate compositions. The LO overtone to fundamental intensity ratio, a rough gauge of exciton-phonon coupling strength, increases considerably for intermediate compositions compared with those of either pure ZnSe or pure CdSe. The results indicate that partial localization of the hole in locally Cd-rich regions of the alloyed particles increases the strengths of local internal electric fields, increasing the coupling between the exciton and polar optical phonons.