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In this article, we provided a numerical simulation for asymptotic normality of a kernel type estimator for the intensity obtained as a product of a periodic function with the power trend function of a nonhomogeneous Poisson Process. The aim of this simulation is to observe how convergence the variance and bias of the estimator. The simulation shows that the larger the value of power function in intensity function, it is required the length of the observation interval to obtain the convergent of the estimator.

A non-perfect maze is a maze that contains loop or cycle and has no isolated cell. A non-perfect maze is an alternative to obtain a maze that cannot be satisfied by perfect maze. This paper discusses non-perfect maze generation with two kind of biases, that is, horizontal and vertical wall bias and cycle bias. In this research, a maze is modeled as a graph in order to generate non-perfect maze using Kruskal algorithm modifications. The modified Kruskal algorithm used Fisher Yates algorithm to obtain a random edge sequence and disjoint set data structure to reduce process time of the algorithm. The modification mentioned above are adding edges randomly while taking account of the edge’s orientation, and by adding additional edges after spanning tree is formed. The algorithm designed in this research constructs an  non-perfect maze with complexity of  where  and  denote vertex and edge set of an  grid graph, respectively. Several biased non-perfect mazes were shown in this research by varying its dimension, wall bias and cycle bias.

Abstract. This paper discusses the steps of constructing simple graphs on graph theory application development. Most graphs constructing on application development use an adjacency matrix and an adjacency list before the graph is constructed. However, it is considerably difficult to construct a graph in such way. The steps of constructing a graph in this work were started by directly construct a graph on stage. The graph was constructed by creating the vertices and every edge can be created after creating two vertices as its endpoint. The graphs can be changed by moving the vertex and deleting vertices and edges. Furthermore, the graph can be changed by adding vertices and edges. The adjacency list is then obtained from the given graph and used for further processes. The steps of constructing graph are interactive so that constructing graph can be made easier and more efficient.

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