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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 subset Sof V (G) is a "double dominating set" for G if S dominates every vertex of G at least twice. The minimum cardinality of a double dominating set is called double domination number and is denoted by γdd. In this paper, the double domination number of central, middle and total graphs of star graph is found. [ABSTRACT FROM AUTHOR]

In graph theory, domination is the major area which attracts researchers due to its potential to solve many real life problems. Particularly, tree dom strong domination solves problems involving design and analysis of communication network and social network. For every v ∈ V - DS where DS is a Dom strong dominating set (Dsd-set), there exists u1, u2 ∈ DS such that u1v, u2v ∈ E(G) and deg(u1) ≥ deg(v). The minimum cardinality of a Dsd-set is denoted by γdsd(G). A Dsd-set of a graph G is a tree dom strong dominating set (trdsd set) if the induced subgraph is a tree. The minimum cardinality taken over all tree dom strong dominating sets is denoted by γtrdsd(G). The sum of the tree dom strong domination number and maximum degree of graphs equal to 2n - 3 is studied and characterized the corresponding extremal graphs. [ABSTRACT FROM AUTHOR]

In this study, an integrated economic order quantity inventory model for deteriorating items with inventory level and ware house capacity constraint is considered. The proposed model allows shortage for buyer and demand to be considered as a constant. By using Lagrange's multiplier technique optimum order quantity is obtained to minimize the system cost while satisfies the both constraints. Numerical examples are also illustrating developed model. [ABSTRACT FROM AUTHOR]