The concept of super line graph was introduced in the year 1995 by Bagga, Beineke and Varma. Given a graph with at least r edges, the super line graph of index r, Lr(G), has as its vertices the sets of r-edges of G, with two adjacent if there is an edge in one set adjacent to an edge in the other set. The line completion number lc(G) of a graph G is the least positive integer r for which Lr(G) is a complete graph. In this paper, we  nd the line completion number of Grid graph Pn  Pm for various cases of n and m.

Introduction: With writing the special code based on Grid search technique, best method for describing the elements energy spectrum is introduced. This method is suitable for investigation of Atomic, molecular and nuclear Energy spectrum, laser pulses and study of spectrum that obtained by laser interaction with cell and human body.Microraman spectrum of eye lens that fitted by De. Mul and time spectrum of one molecule that excited by 585 nm laser and fitted by Gnu plot software. In a special application, this method is used for 22Na spectrums.Material and Methods: For fitting mathematical function to a set of experimental data, the first step is seeing data plot in every software. Then, an initial mathematical function is guessed and the function parameters change as far as possible for initial fitting. After this step, by using this special code based on Grid search technique, is the X2 changes between function data and experimental data are compared. If the X2 is high, it will reduce by introducing small change in every parameter of mathematical function. This is done step, by step, so the X2 reaches to the lowest.Results: By this method, we can have the formulation of element energy spectrum. For example, the equation of 22Na energy spectrum’s description with least squares fitted by experiment data is: N=199.0477 +76100EXP (0.00167 (E-508.7539) 2) + 75100EXP (0.00168 (E-509.2428) 2) + 3450.8070 EXP (0.0000831(E-655.356) 2) + 4002.813EXP (0.0001431(E-839.401) 2) + 11000EXP (0.00105 (E-1048.0230) 2) Fitting start with fit parameter X2=1107.6 and finished with X2 =44.16.Conclusion: By using the special code based on Grid search technique, we try to introduce the best method for describing of the elements energy spectrum.

The Grid is an emerging technology for enabling resource sharing and coordinated problem solving in dynamic multi-institutional virtual organizations. This paper presents algorithms, methods, and software for a Grid resource manager, responsible for resource brokering and scheduling in Grids. The broker selects computing resources based on actual job requirements and a number of criteria identifying the available resources, with the aim to minimize the turnaround time for the individual application. In pervious work, we proposed Grid-JQA [8] [9]. In this work we propose an aggregation formula for the QoS parameters. The formula is a unit less combination of the parameters together with weighting factors. It is shown that the formula needs to put into a threshold consideration. A discussion on the threshold and its level is also provided. The paper is finalized by the results obtained from simulation and a comparison study.

The independence graph Ind(G) of a graph G is the graph with vertices as maximum independent sets of G and two vertices are adjacent, if and only if the corresponding maximum independent sets are disjoint. In this work, we find the independence graph of Cartesian product of d copies of complete graphs Kq, which is known as the Hamming graph H(d, q). Greenwell and Lovasz [7] found that the independence number of direct product of d copies of Kq as qd−1. We prove that the independence number of Hamming graph H(d, q), which is cartesian product of d copies of Kq, is also qd−1. As an application of our findings, we find answers for rook problem in higher dimensional square chess board.

This paper proposes a new traveling wave-based fault location method for power transmission Grids. The proposed method involves an online and an offline stage. In the offline stage, the transmission network is represented by a weighted graph. The shortest paths between any two sensors are determined. The branches of the graph that are not on at least one of the shortest path, are divided into virtual lines associated with the location of the sensors. In the online stage, according to first arrival time at different sensors, the points belonging to the shortest paths obtained during the offline stage with the possibility of having a fault are identified Then using an evaluation index, the exact point of fault and the fault inception time are determined. The proposed method is independent of the fault type and can be utilized in transmission network with any size. Simulation studies carried out using EMTP software and MATLAB, verify high accuracy of the proposed method.

In this paper, we find the star chromatic number of central graph of complete bipartite graph and corona graph of complete graph with path and cycle.

Let R be a commutative ring and M be an R-module. The M-intersection graph of ideals of R, denoted by GM(R) is a graph with the vertex set I(R) ∗, , and two distinct vertices I and J are adjacent if and only if IM ∩,JM ̸, = 0. In this paper, we study GR/J (R/I), where I and J are ideals of R and I ⊆,J. We characterize all ideals I and J for which GR/J (R/I) is planar, outerplanar or ring graph.