What is spectral graph theory used for?

Spectral graph theory has applications to the design and analysis of approximation algorithms for graph partitioning problems, to the study of random walks in graph, and to the construction of expander graphs.

Is a spectrum a graph?

While the adjacency matrix depends on the vertex labeling, its spectrum is a graph invariant, although not a complete one. Spectral graph theory is also concerned with graph parameters that are defined via multiplicities of eigenvalues of matrices associated to the graph, such as the Colin de Verdière number.

What is graph theory for kids?

Graph theory is a field of mathematics about graphs. A graph is an abstract representation of: a number of points that are connected by lines. Each point is usually called a vertex (more than one are called vertices), and the lines are called edges. Graphs are a tool for modelling relationships.

Which of the following property of a graph can be determined from its spectrum?

Which graphs are determined by their spectrum? (exponents indicate multiplicities). For graphs on less than five vertices, no pair with cospectral adjacency matrices exists, so each of these graphs is determined by its spectrum.

What is spectral chart?

The spectral distribution chart is a visual representation of the light spectrum produced by a lamp. It is a graph showing the relative intensities of a light source at each wavelength. These charts can be used to compare the energy levels of various light sources.

What is spectrum short?

1 : the group of colors that a ray of light can be separated into including red, orange, yellow, green, blue, indigo, and violet : the colors that can be seen in a rainbow beautiful scarves in all the colors of the spectrum. 2 technical : an entire range of light waves, radio waves, etc.

What is a spectrum in physics?

spectrum, in optics, the arrangement according to wavelength of visible, ultraviolet, and infrared light. Spectra may be classified according to the nature of their origin, i.e., emission or absorption.

What graphs are determined by the spectrum?

Many distance-regular graphs are known to be determined by their parameters, and some of these are also determined by their spectrum (see Section 6). We assume familiarity with basic results from linear algebra, graph theory, and combinatorial matrix theory.