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A signed graph is the special kind of gain graph in which the gain group has order 2. The pair (G, B(Σ)) determined by a signed graph Σ is a special kind of biased graph. The sign group has the special property, not shared by larger gain groups, that the edge signs are determined up to switching by the set B(Σ) of balanced cycles. [19]
A pair of graphs are said to be cospectral mates if they have the same spectrum, but are non-isomorphic. 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 ...
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 ...
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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.
The cycle of length 5 is an srg(5, 2, 0, 1). The Petersen graph is an srg(10, 3, 0, 1). The Clebsch graph is an srg(16, 5, 0, 2). The Shrikhande graph is an srg(16, 6, 2, 2) which is not a distance-transitive graph. The n × n square rook's graph, i.e., the line graph of a balanced complete bipartite graph K n,n, is an srg(n 2, 2n − 2, n − ...
Correction to GMRS power level 462 MHz interstitial (2 to 5 watts) 22:01, 24 March 2022: 512 × 640 (12 KB) Mckoss: Add solid (white) background - instead of transparency. 00:28, 20 March 2022: 512 × 640 (12 KB) Mckoss: Added key/legend: 23:49, 19 March 2022: 512 × 640 (11 KB) Mckoss: Corrected power limits for FRS above 467 MHz: 23:40, 19 ...
The Coxeter graph is also uniquely determined by its graph spectrum, the set of graph eigenvalues of its adjacency matrix. [ 8 ] As a finite connected vertex-transitive graph that contains no Hamiltonian cycle , the Coxeter graph is a counterexample to a variant of the Lovász conjecture , but the canonical formulation of the conjecture asks ...