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In the area of graph theory in mathematics, a signed graph is a graph in which each edge has a positive or negative sign. A signed graph is balanced if the product of edge signs around every cycle is positive. The name "signed graph" and the notion of balance appeared first in a mathematical paper of Frank Harary in 1953. [1]
In condensed matter physics, Hofstadter's butterfly is a graph of the spectral properties of non-interacting two-dimensional electrons in a perpendicular magnetic field in a lattice. The fractal, self-similar nature of the spectrum was discovered in the 1976 Ph.D. work of Douglas Hofstadter [ 1 ] and is one of the early examples of modern ...
The smallest pair of cospectral mates is {K 1,4, C 4 ∪ K 1}, comprising the 5-vertex star and the graph union of the 4-vertex cycle and the single-vertex graph [1]. The first example of cospectral graphs was reported by Collatz and Sinogowitz [2] in 1957. The smallest pair of polyhedral cospectral mates are enneahedra with eight vertices each ...
A common format is a graph with two geometric dimensions: one axis represents time, and the other axis represents frequency; a third dimension indicating the amplitude of a particular frequency at a particular time is represented by the intensity or color of each point in the image.
In graph theory, a signed graph is a graph in which each edge has been marked with a positive or negative sign. In mathematical analysis, a signed measure is a generalization of the concept of measure in which the measure of a set may have positive or negative values. The concept of signed distance is used to convey side, inside or out.
A FedEx contract worker has been busted for allegedly dumping dozens of packages in the woods to avoid working late. Latavion Lewis was arrested after a post office in Bonifay, Florida, received ...
In late July, Super Micro's auditor at the time, Ernst & Young (EY), raised concerns about the company's governance, transparency and internal control over financial reporting, prompting its board ...
Spectral shape analysis relies on the spectrum (eigenvalues and/or eigenfunctions) of the Laplace–Beltrami operator to compare and analyze geometric shapes. Since the spectrum of the Laplace–Beltrami operator is invariant under isometries, it is well suited for the analysis or retrieval of non-rigid shapes, i.e. bendable objects such as humans, animals, plants, etc.
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