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In this paper we will introduce a new graph distance based polynomial; Detour Hosoya polynomials of graphs ) x ; G ( H * . The Detour Hosoya polynomials ) x ; G ( H * for some special graphs such as paths and cycles are obtained. Moreover the Detour Hosoya polynomials ) x ; G G ( H * 2 1 • , 12 * H ( G :G;x) and 12  * H ( G G;x) are obtained.

Detour Hosoya Polynomials of Some Compound Graphs