Is the superlative of the adjective sparse, sparsest or most sparse? Can both be used? If not, then which one is correct?
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Sparsest would be the correct form. Nevertheless, a quick peek in a dictionary could have provided you with this answer.
They're actually both correct depending on context. Google Ngram Viewer shows a substantial number of hits for "most sparse", e.g., "the AEC algorithm outcome is the distance between points in the most sparse clusters".
While the normal superlative is "sparsest", in a list of superlatives, you will probably want to use parallel structure so that all are in the same form, e.g., "X is the most interesting, traditional, and sparse of the options".
"Correct" is often a relative concept, especially with natural language.
The word sparsest is the correct choice of expression. The number of syllable in the adjective (or adverb) determines if the superlative should end with the suffix "-est" or begin with the adverb "most". When it has only one syllable (e.g. sparse), or two but ends with the letter "y" (e.g. happy), the suffix "-est" should be used to form the superlative (e.g. sparsest, happiest), or else we use the adverb "most" (e.g. most peaceful, most horrific).
Note: there are cases where the rules above do not apply. (e.g. good & best, bad & worst)