Results 271 to 280 of about 841,611 (282)

Spectra of quaternion unit gain graphs

Linear Algebra and its Applications, 2022
Abstract A quaternion unit gain graph is a graph where each orientation of an edge is given a quaternion unit, which is the inverse of the quaternion unit assigned to the opposite orientation. In this paper we define the adjacency, Laplacian and incidence matrices for a quaternion unit gain graph and study their properties.
Belardo F., Brunetti M., Coble N. J., Reff N., Skogman H.   +4 more
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GRAPHS DETERMINED BY THEIR -GAIN SPECTRA

Bulletin of the Australian Mathematical Society, 2020
AbstractAn undirected graph $G$ is determined by its $T$-gain spectrum (DTS) if every $T$-gain graph cospectral to $G$ is switching equivalent to $G$. We show that the complete graph $K_{n}$ and the graph $K_{n}-e$ obtained by deleting an edge from $K_{n}$ are DTS, the star $K_{1,n}$ is DTS if and only if $n\leq 2$, and an odd path $P_{2m+1}$ is not ...
SAI WANG, DEIN WONG, FENGLEI TIAN
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Lock-Gain Based Graph Partitioning

Journal of Heuristics, 2004
We propose a new heuristic for the graph partitioning problem. Based on the traditional iterative improvement framework, the heuristic uses a new type of gain in selecting vertices to move between partitions. The new type of gain provides a good explanation for the performance difference of tie-breaking strategies in KL-based iterative improvement ...
Yong-Hyuk Kim, Byung-Ro Moon
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Subgroup Switching of Skew Gain Graphs

Fundamenta Informaticae, 2012
Gain graphs are graphs in which each edge has a gain (a label from a group so that reversing the direction of an edge inverts the gain). In this paper we take a generalized view of gain graphs in which the gain of an edge is related to the gain of the reverse edge by an anti-involution, i.e., an anti-automorphism of order at most two.
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Inertia of complex unit gain graphs

Applied Mathematics and Computation, 2015
Let T = { z ? C : | z | = 1 } be a subgroup of the multiplicative group of all nonzero complex numbers C × . A T -gain graph is a triple ? = ( G , T , ? ) consisting of a graph G = ( V , E ) , the circle group T and a gain function ? : E ? ? T such that ? ( e i j ) = ? ( e j i ) - 1 = ? ( e j i ) ? . The adjacency matrix A(?) of the T -gain graph ? = (
Jianhua Tu, Guihai Yu, Hui Qu
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Complex unit gain graphs of rank 2

Linear Algebra and its Applications, 2020
Abstract Let T be the group of all complex numbers z with | z | = 1 . A complex unit gain graph, or simply a T -gain graph, is a triple Φ = ( G , T , φ ) consisting of a graph G = ( V , E ) , the circle group T and a gain function φ : E → → T such that φ ( v i v j
Feng Xu, Qi Zhou, Dein Wong, Fenglei Tian   +3 more
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Evaluating the gain of a flow graph by the Grassmann algebra

International Journal of Control, 1984
The outgoing branches from a node of Coates' flow graph are interpreted as the elements of column vectors of the system matrix. The Grassmann algebra is used to calculate the exterior or outer product of these column vectors for evaluating the system determinant.
C. F. Chen, M. B. Ahmad
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Construction of cospectral graphs, signed graphs and $${\mathbb {T}}$$-gain graphs via partial transpose

Journal of Algebraic Combinatorics
In the wake of Dutta and Adhikari, who in 2020 used partial transposition in order to get pairs of cospectral graphs, we investigate partial transposition for Hermitian complex matrices. This allows us to construct infinite pairs of complex unit gain graphs (or T-gain graphs) sharing either the spectrum of the adjacency matrix or even the spectrum of ...
Belardo F., Brunetti M., Cavaleri M., Donno A.   +3 more
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