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For the most part, vendor adopts quantity discount to the buyer to motivate retailers to make bigger orders. The subject of this paper is the problem of observing ideal recharging strategy for a stock, dependent upon quantity discount and deterioration. It is shown that considering restriction truly influences the course of action of the issue. At long last, mathematical model is displayed to show the ordinary use of the proposed model. [ABSTRACT FROM AUTHOR]

A total coloring of a graph is a coloring to the elements (vertices and edges) of thegraphG, for which any adjacent vertices or edges and incident elements are colored differently. The total chromatic number of G is the minimum number of colors that needed in a total coloring. In this paper, we have determined the total chromatic number for pan graph, double wheel graph and double crown graph. [ABSTRACT FROM AUTHOR]