For any group G, we define G/H (read” G mod H”) to be the set of left cosets of H in G and this set forms a group under the operation (a)(bH) = abH. The character table of rational representations study to gain the K( SL(2,81)) and K( SL(2, 729)) in this work.
(10)
(7)
(3)
(4)
(3)
(2)
(3)
(1)
(3)
(1)
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.