In graph theory a partition of the vertex set of a graph is called equitable if for all pairs of cells all vertices in one cell have an equal number of neighbours in the other cell. Considering the implications for the adjacency matrix one may generalize that concept as a block partition of a complex square matrix s.t. each block has constant row sum. It is well known that replacing each block ...

Spectral graph theory looks at the interplay between the structure of a graph and the eigenvalues of a matrix associated with the graph. Many interesting graphs have rich structure which can help in determining the eigenvalues associated with some particular matrix of a graph. This survey looks at some common techniques in working with and determining the eigenvalues associated with the normali...

For any simple connected undirected graph, it is well known that the Kirchhoff and multiplicative degree-Kirchhoff indices can be computed using the Laplacian matrix. We show that the same is true for the additive degree-Kirchhoff index and give a compact Matlab program that computes all three Kirchhoffian indices with the Laplacian matrix as the only input.

A wind farm is a collection of wind turbines built in an area to provide electricity. Wind power is a renewable energy resource and an alternative to non-renewable fossil fuels. In this paper impact of wind farms in power system reliability is investigate and a new procedure for reliability assessment of wind farms in HL1 level is proposed. In proposed procedure, application of Fuzzy – Markov f...

In this paper, we review the problem of matrix completion and expose its intimate relations with algebraic geometry, combinatorics and graph theory. We present the first necessary and sufficient combinatorial conditions for matrices of arbitrary rank to be identifiable from a set of matrix entries, yielding theoretical constraints and new algorithms for the problem of matrix completion. We conc...

This manuscript will provide a step by step method on how a graph theory and topology can be utilized to construct a Z-loop matrix for the study of faulted 3 phase power systems. The growing demand for reliable electrical power supply has forced the pace developments in electrical power system analysis using computer. In this, power system analysis plays a significant role for the analysis of f...

In order to take into account the influence of both system structure and diagnosis algorithm in diagnosability design system, a diagnosability-integrated method based on graph theory was proposed this paper. Firstly, evaluation results, difficulty fault qualitatively analyzed using K-means method, plot measurement point drawn analysis results. Secondly, Bron–Kerbosch used extract maximal clique...

In this research paper, we use a normalized graph cut measure as a thresholding principle to separate an object from the background based on the standard S membership function. The implementation of the proposed algorithm known as fuzzy normalized graph cut method. This proposed algorithm compared with the fuzzy entropy method [25], Kittler [11], Rosin [21], Sauvola [23] and Wolf [33] method. M...