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AbstractThe perfect parking lot will avoid confusion in parking vehicles. Parking lot problems deal with a lot of real-life challenges like the shape of the parking lot, angle of parking, the dimension of vehicles and available area. Parking space should allow the maximum number of vehicles to be parked. A mathematical model can be created to maximize the number of vehicles to be parked. Also, the mathematical model should subject to challenging constraints. In this paper, the mathematical model of the parking lot in the regular octagon-shaped parking area using the concept area of rectangle and the right triangle is developed. To illustrate the mathematical model, the regular octagon-shaped parking area is taken and also LINGO software is used to solve the problem.

AbstractGraph theory concepts applicable in more real life problems. The 3rddimensional product of vertex measurable graph is applicable in supply chain network. Assigning secondary warehouses and maintaining the selling stores plays important role in supply chain network. In this paper, the mathematical model of 3rddimensional product of vertex measurable graph is developed and the numerical example is taken to illustrate the model.

AbstractThe main result of this paper is the following: we show that if for a left symmetric algebra there exists a finite strictly ascending chain (or sequence) of two side ideals and the square of each element of an ideal is in the preceding one, then the algebra is nilpotent.

AbstractConsider a simple connected graph G(V, E), a set S is a dominating set if for every vertex uϵ V – S, there exists a vertex vϵ Ssuch that uis adjacent to v. i.e. for every vertex uϵ V – S, d(u, S) = 1. A dominating set Din Gis a minimal dominating set if no proper subset of Dis a dominating set. The minimum cardinality among all the minimal dominating sets is called domination number of the graph Gdenoted by g(G). Let be three simple non trivial connected graph. The 3rd dimension product of vertex measurable graphs of G1, G2, G3denoted by G1× G2× G3is a graph with vertex set . Such that two vertices a= (u1, v1, w1) and b= (u2, v2, w2) are said to be adjacent if u1= u2where v1v2ϵ and w1w2ϵ or v1= v2where u1u2ϵ and w1w2ϵ or w1= w2where u1u2ϵ and v1v2ϵ . In this paper we introduce few extended definitions of 3rd dimensional product of vertex measurable graphs, apply the concept of domination sets for 3rd dimension product of vertex measurable graphs with G1, G2, G3having two vertices