In a connected graph , the distance function between each pair of two vertices from a set vertex  is the shortest distance between them and the vertex degree  denoted by  is the number of edges which are incident to the vertex  The Schultz and modified Schultz polynomials of  are have defined as:  respectively, where the summations are taken over all unordered pairs of distinct vertices in  and  is the distance between  and  in  The general forms of Schultz and modified Schultz polynomials shall be found and indices of the edge – identification chain and ring – square graphs in the present work.

In a connected graph G, the distance function between each pair of two vertices from a set vertex V(G) is a shortest distance between them and the vertex degree v, deg v, is the number of edges which are incident to the vertex v. The Schultz and modified Schultz polynomials of G are have defined as :Sc(G; x) = ∑( deg v + deg u) x d (u, v) and Sc ∗ (G; x) = ∑ (deg v. deg u) x d (u, v), respectively, where the summations are taken over all unordered pairs of distinct vertices in V(G) and d(u, v) is the distance between u and v in V(G). We shall find the general forms of Schultz and modified Schultz polynomials and indices of the edge – identification chain and ring – pentagon and hexagon graphs in the present work.

The aim of this paper is to find polynomials related to Schultz, and modified Schultz indices of vertex identification chain and ring for hexagonal rings (6cycles). Also to find index and average index of all of them.

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G OSSYPOL is a poisonous yellow polyphenolic pigment found in cotton plants (Gossypium spp.), which inhibits animal reproduction. Gossypol also affects steroidogenesis, nuclear maturation, follicular size, granulosa cell proliferation, and steroidogenic activity. Therefore, we aimed to examine the effect of gossypol on rat ovarian physiology and detect the probable beneficial effects of quercetin and curcumin. Forty-eight female albino rats were divided into six groups: control, gossypol, quercetin, curcumin, (gossypol and quercetin), and (gossypol and curcumin) were administered orally at different doses for 35 days. The results showed that gossypol significantly decreased body, ovarian and uterine weights, whereas, neither quercetin or curcumin treatments with gossypol showed any significant improvement in body, ovarian, and uterine weight compared to the gossypol group. Gossypol group showed the highest number of growing ovarian follicles compared with the control group. The two groups of quercetin, curcumin with gossypol showed a significant increase in the antral ovarian follicles compared with gossypol treatment. This study concluded that gossypol had negative effects on body, uterus and ovaries which led to a decrease in their weights. In addition, the use of antioxidants (quercetin or curcumin) with these doses and duration of the treatment has minor effects to reverse or ameliorate gossypol harmful effects.