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In 1978 , Chao and Whitehead defines a color map is unique, if it's any other color diagram polynomials and are not the same . As we all know , the chromatic polynomial is the study of color graphs important tool since 1978 in this area have developed a large number of results . P points on the map with G, set G 0 is a spanning subgraph of G , if G 0 are each branch of a complete graph , then G 0 is called the ideal subgraph . So b i (G) having in mind the ideal pi subgraph branch number , apparently b 0 (G) = 1, b 1 (G) = q (G). in 1987, Liu Ru Ying adjoint polynomials defined as follows : h (G, x) = Σ k = 0 p-1 b i (G) x pi . for simplicity , we will h (G, x) denoted by h (G). we call accompanying two graphs G and H such price, if h (G, x) = h (H, x). adjoint polynomials introduced successfully studied chromatic uniqueness . Hosoya- topological index is an important parameter, which in the study of molecular structure and physical organic chemistry , for example , boiling point , thermal contact have an important role in the article, we will use it to solve the chromatic uniqueness in chemistry to study molecular graphs heat makes sense because it can be the graph Ji - electronic energy that refs [ 21,22 ] , we already know that the success of the introduction of adjoint polynomials of the chromatic uniqueness, in fact many of its properties in the comparison of different molecular size chart is very useful thermal energy . In this article, I use the Hosoya- indicators and study the properties of adjoint polynomials of some graphs chromatic uniqueness , with the adjoint polynomial of a class tree great energy .
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