The Distance matrix, Distance eigenvalue, and Distance Energy of a connected graph have been studied in detail in literature where as the study on Distance Seidel matrix associated with a connected graph is in progress. The eigenvalues ∂ S 1 ≥ ∂ S 2 >. . . ∂S n of the Distance Seidel matrix D S (G) of a graph G forms the Distance Seidel spectrum of G. We describe here the Distance Seidel spectrum of some types of subdivision related graphs of a regular graph in terms of its adjacency spectrum. We also derive analytic expressions for the Distance Seidel Energy of S¯(Cp), the partial complement of the subdivision graph of a cycle Cp and the Distance Seidel Energy of S(Cp), the complement of the even cycle C2p

Let S(G) be the Seidel matrix of a graph G of order n and let DS(G) = diag(n 􀀀 1 􀀀 2d1; n 􀀀 1 􀀀 2d2; : : :; n 􀀀 1 􀀀 2dn) be the diagonal matrix with di denoting the degree of a vertex vi in G. The Seidel Laplacian matrix of G is defined as SL(G) = DS(G) 􀀀 S(G) and the Seidel signless Laplacian matrix as SL+(G) = DS(G) + S(G). The Seidel signless Laplacian Energy ESL+(G) is defined as the sum of the absolute deviations of the eigenvalues of SL+(G) from their mean. In this paper, we establish the main properties of the eigenvalues of SL+(G) and of ESL+(G).

In the paper we consider a generalized join operation, that is, the H-join on graphs where H is an arbitrary graph. In terms of Seidel matrix of graphs we determine the Seidel spectrum of the graphs obtained by this operation on regular graphs. Some additional consequences regarding S-integral complete split graphs are also obtained, which allows to exhibit many infinite families of Seidel integral complete split graphs.

Let G be a simple graph with n vertices and with the Seidel matrix S. Suppose  1;  2; : : :;  n are the Seidel eigenvalues of G. The Estrada index of the Seidel matrix of G is defined as SEE(G) = Σ n i=1 e i. In this paper, we compute the Estrada index of the Seidel matrix of some known graphs. Also, some bounds for the Seidel Energy of graphs are given.

Distance-based clustering methods categorize samples by optimizing a global criterion, finding ellipsoid clusters with roughly equal sizes. In contrast, density-based clustering techniques form clusters with arbitrary shapes and sizes by optimizing a local criterion. Most of these methods have several hyper-parameters, and their performance is highly dependent on the hyper-parameter setup. Recently, a Gaussian Density Distance (GDD) approach was proposed to optimize local criteria in terms of Distance and density properties of samples. GDD can find clusters with different shapes and sizes without any free parameters. However, it may fail to discover the appropriate clusters due to the interfering of clustered samples in estimating the density and Distance properties of remaining unclustered samples. Here, we introduce Adaptive GDD (AGDD), which eliminates the inappropriate effect of clustered samples by adaptively updating the parameters during clustering. It is stable and can identify clusters with various shapes, sizes, and densities without adding extra parameters. The Distance metrics calculating the dissimilarity between samples can affect the clustering performance. The effect of different Distance measurements is also analyzed on the method. The experimental results conducted on several well-known datasets show the effectiveness of the proposed AGDD method compared to the other well-known clustering methods.

A graph which does not contain C4, P4, or 2K2 as its induced subgraphs, is called a threshold graph. In this paper, we consider Seidel laplacian matrix of a connected threshold graph and determine the Seidel laplacian spectrum. Also, the characterization of threshold graphs having atmost four distinct Seidel laplacian eigenvalues have been computed.

In this research, By using data envelopment analysis method and output Distance functions to decomposes Energy productivity change into four components; technical efficiency change, technological change, changes in capital to Energy ratio and labor in Energy ratio In the industrial sector of the country Iran during the period 2014-2004. To this end, the output-axis data envelope analysis method has been used with the assumption of constant returns to scale. The results show that the effect of changing the ratio of capital to Energy is a major factor in reducing the of Energy intensity in the industrial sector of the Iran, changes technological progress, changes labor-Energy ratio and changes technical efficiency drove up Energy intensity in most industries.

Let D be the diameter and dG(vi, vj ) be the Distance between the vertices vi and vj of a connected graph G. The complementary Distance matrix of a graph G is CD(G) = [cdij ] in which cdij = 1 +D − dG(vi, vj ) if i 6= j and cdij = 0 if i = j. The complementary transmission CTG(v) of a vertex v is defined as CTG(v) = Pu2V (G)[1+D− dG(u, v)]. Let CT(G) = diag[CTG(v1), CTG(v2), . . ., CTG(vn)]. The complementary Distance signless Laplacian matrix of G is CDL+(G) = CT(G) + CD(G). In this paper, we obtain the bounds for the largest eigenvalue of CDL+(G). Further we determine Nordhaus-Gaddum type results for the largest eigenvalue. We also establish some bounds for the complementary Distance signless Laplacian Energy.

This research focuses on the effect of passive methods in the field of Energy storage, produce Energy by using renewable energies, and also to achieve the construction patterns of residential buildings in the climate conditions of Shiraz, with the aim reducing Energy consumption. Statistics show that in Iran, fuel consumption in residential and commercial buildings with an average annual growth of 7. It is about 2.37% of the country's total fuel consumption. One way to minimize Energy consumption in this sector is to increase the role of zero-Energy buildings. Zero-Energy buildings provide technical ways to consume less Energy in buildings. These buildings are designed and built so that all or a large part of these provide the Energy they need through the combination of Energy saving and the use of renewable Energy technology. In this research, after studying the climate condition of the city of Shiraz, a building in the Energy Plus software, the simulation and climatic data of the Shiraz station was introduced to the software. To achieve the most optimal conditions of Energy consumption in the climatic conditions of Shiraz, each of the building elements Residential was optimized. The simulation shows that it is possible to reduce the Energy consumption of the building by using passive building materials and designs, including double-glazed glass, Wall insulation, etc. On the other hand, by using solar Energy, using pvsyst software, you can supply the Energy needed by the building.