Results 31 to 40 of about 3,672,970 (235)
Matroids of gain graphs in applied discrete geometry [PDF]
Transactions of the American Mathematical Society, 2015 A Γ \Gamma -gain graph is a graph whose oriented edges are labeled invertibly from a group Γ \Gamma . Zaslavsky proposed two matroids associated with Γ \Gamma -gain graphs, called frame matroids and lift matroids, and investigated linear representations of them.
Shin‐ichi Tanigawa
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Godsil-McKay switchings for gain graphs
The Electronic Journal of Linear AlgebraWe introduce a switching operation, inspired by the Godsil-McKay switching, in order to obtain pairs of $G$-cospectral gain graphs, that are gain graphs cospectral with respect to every representation of the gain group $G$. For instance, for two signed graphs, this notion of cospectrality is equivalent to the cospectrality of their signed adjacency ...
Matteo Cavaleri +2 more
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On the Characteristic Polynomial of Skew Gain Graphs
, 2020 Gain graphs are graphs where the edges are given some orientation and labeled with the elements (called gains) from a group so that gains are inverted when we reverse the direction of the edges. Generalizing the notion of gain graphs, skew gain graphs have the property that the gain of a reversed edge is the image of edge gain under an anti-involution.
Hameed, K. Shahul +3 more
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Spectral Properties of Dual Unit Gain Graphs [PDF]
SymmetryIn this paper, we study dual quaternion, dual complex unit gain graphs, and their spectral properties in a unified frame of dual unit gain graphs. Unit dual quaternions represent rigid movements in the 3D space, and have wide applications in robotics and
Chunfeng Cui +3 more
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Incidence Gain Graphs and Generalized Quadrangles [PDF]
We demonstrate a construction method based on a gain function that is defined on the incidence graph of an incidence geometry. Restricting to when the incidence geometry is a linear space, we show that the construction yields a generalized quadrangle provided that the gain function satisfies a certain bijective property.
Ryan McCulloch
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An interaction graph approach to gain new insights into mechanisms that modulate cerebrovascular tone [PDF]
Communications BiologyMechanisms to modulate cerebrovascular tone are numerous, interconnected, and spatially dependent, increasing the complexity of experimental study design, interpretation of action-effect pathways, and mechanistic modelling. This difficulty is exacerbated
Sergio Dempsey +3 more
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On the spectrum of complex unit gain graph
, 2019 A $\mathbb{T}$-gain graph is a simple graph in which a unit complex number is assigned to each orientation of an edge, and its inverse is assigned to the opposite orientation. The associated adjacency matrix is defined canonically, and is called $\mathbb{T}$-gain adjacency matrix.
Samanta, Aniruddha, Kannan, M. Rajesh
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Line graphs of complex unit gain graphs with least eigenvalue -2
The Electronic Journal of Linear Algebra, 2021 Let $\mathbb T$ be the multiplicative group of complex units, and let $\mathcal L (\Phi)$ denote a line graph of a $\mathbb{T}$-gain graph $\Phi$. Similarly to what happens in the context of signed graphs, the real number $\min Spec(A(\mathcal L (\Phi))$, that is, the smallest eigenvalue of the adjacency matrix of $\mathcal L(\Phi)$, is not less than $-
Belardo F., Brunetti M.
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The rank of a complex unit gain graph in terms of the matching number [PDF]
Linear Algebra and its Applications, 2019 Shengjie He, Rongxia Hao, F. Dong
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A Mathematical Bibliography of Signed and Gain Graphs and Allied Areas [PDF]
The Electronic Journal of Combinatorics, 2018 A signed graph is a graph whose edges are labeled by signs. This is a bibliography of signed graphs and related mathematics.Several kinds of labelled graph have been called "signed" yet are mathematically very different. I distinguish four types:Group-signed graphs: the edge labels are elements of a 2-element group and are multiplied around a polygon ...
Thomas Zasĺavsky
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