iosr-Jm   Volume-2 ~ Issue-6

Abstract :We have endeavoured here to depict an interactive inventory model between producer (supplier) and prospective buyer (vendor) in the presence of an extraordinary purchase and credit period with two parameter weibull deterioration for items with ramp type demand. The case of shortages is also studied.Additonally, we deal with the problem of a supplier disposing a large inventory level through an offer to a prospective buyer in the form of a credit period. From our model we confirm that the behaviour of replenishment period and trade credit period and change of the total variable cost observed from numerical evidence should be interpreted with caution in any business organisation.
Keywords: credit period, ramp type demand , shortages, Weibull deterioration

[1] WU Kun-Shan, An EOQ inventory model for items with weibull distribution deterioration, ramp type demand rate and partial backlogging, Production Planning and control, 12(2001), 787-793.
[2] Sanjay Jain and Kumar Mukesh ,An EOQ Inventory model with ramp type demand, weibull distribution deterioration and starting with shortage, OPSARCH Vol.44(2007), 240-250.
[3] T.Chakrabarty, B.C. Giri,. and K.S.Chaudhury, An EOQ Inventory Model for items with weibull distribution deterioration, shortages and trended demand: An extension of Philip's model, Computers and Operations Research, 25(1998), 649-657.
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[5] N.H.Shah, and Y.K.Shah, A Discrete-In-Time Probabilistic Inventory Model for Deteriorating Items under conditions of Permissible delay in Payment, International Journal of System Science, 29(1998), 121-126.
[6] S.P.Aggarwal, and C.K.Jaggi, Ordering policies of Deteriorating items under conditions of permissible delay in payments. Journal of operational research society, 46(1995), 658-662.
[7] Manisha Pal, And K.Sanjay Ghosh, An Inventory model with stock dependent demand and general rate of deterioration under conditions of permissible delay in payments,vol.44( 2007), OPSEARCH, 227-239.
[8] S. Hardik., J.Shah, Bhavin and H.Shah Nita.: An EOQ model for deteriorating items with progressive payment sheme under DCF approach, Vol.43(2006), OPSEARCH, 238-257.
[9] A.M.M. Jamal, B.R Sarkar, S.Wang, Optimal payment time for a retailer under permitted delay payments by the wholesaler. International Journal of Production Economic 66(2000), 59-66.
[10] G.Padmanabhan, and P.Vrat, EOQ model for permissible items under stock dependent selling price, European Journal of operational Research, 8.

Abstract:In this paper we study about the prime square dominating graph and we observe that a prime dominating graph need not be prime square dominating graph, but every prime square dominating graph is prime dominating graph. In this paper we got interesting characteristics theorems such as if a graph contains an odd cycle then it is not a prime square dominating graph, if graph is bipartite then it is a prime square dominating graph. Moreover we discussed about minimal prime square dominating graph and provide necessary examples.
Keywords: Dominating graph, Prime dominating graph, Prime Square Dominating graph, minimal dominating, minimal prime square dominating graphs.

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Abstract: Number Theory is one of the oldest branches of mathematics, which inherited rich contributions from almost all greatest mathematicians, ancient and modern. Nathanson [1] was the pioneer in introducing the concepts of Number Theory, particularly, the "Theory of Congruences‟ in Graph Theory, thus paving way for the emergence of a new class of graphs, namely "Arithmetic Graphs". Inspired by the interplay between Number Theory and Graph Theory several researchers in recent times are carrying out extensive studies on various Arithmetic graphs in which adjacency between vertices is defined through various arithmetic functions.
Keywords: Arithmetic graph, Domination, Total domination, Independent domination, Connected domination.

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Abstract: In this paper consider a classical model of stellar explosion ,in a conducting gas of self gravitating gas propagating in a non uniform atmosphere. Similarity principle has been used to reduced the equation governing the flow to ordinary differential equation . Analytical solution of this classical model have been investigated .

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