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In this paper we used Hosoya polynomial ofgroupgraphs Z1,...,Z26 after representing each group as  graph and using Dihedral group to"encrypt the plain texts with the immersion property which provided Hosoya polynomial to immerse the cipher text in another"cipher text to become very"difficult to solve.

Cryptography by Using"Hosoya"Polynomials for"Graphs Groups of Integer Modulen and"Dihedral Groups with'Immersion"Property