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Inertia of complex unit gain graphs
Applied Mathematics and Computation, 2015zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Yu, Guihai, Qu, Hui, Tu, Jianhua
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Spectra of quaternion unit gain graphs
Linear Algebra and Its Applications, 2022A 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.
Francesco Belardo +4 more
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Discrete Mathematics, 2020
The work of Wang et al. (2020) established an upper bound on the multiplicity of a real number as an adjacency eigenvalue of an undirected simple graph G according to the dimension of its cycle space and the number of its pendants. The work of Cardoso et
Shuchao Li, Wei Wei
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The work of Wang et al. (2020) established an upper bound on the multiplicity of a real number as an adjacency eigenvalue of an undirected simple graph G according to the dimension of its cycle space and the number of its pendants. The work of Cardoso et
Shuchao Li, Wei Wei
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Bounds of nullity for complex unit gain graphs
Linear Algebra and its ApplicationszbMATH Open Web Interface contents unavailable due to conflicting licenses.
Chen, Qian-Qian, Guo, Ji-Ming
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Relation between the inertia indices of a complex unit gain graph and those of its underlying graph
Linear and Multilinear Algebra, 2020A T -gain graph is a triple Φ = ( G , T , ϕ ) consisting of an underlying graph G = ( V ( G ) , E ( G ) ) , the circle group T = { z ∈ C : | z | = 1 } and a gain function ϕ : E → → T , such that ϕ ...
Shahid Zaman, Xiaocong He
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Bounds for the rank of a complex unit gain graph in terms of its maximum degree
Linear Algebra and its Applications, 2021zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Lu, Yong, Wu, Jingwen
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Linear and Multilinear Algebra, 2020
Let G ϕ be an n-vertex complex unit gain graph and let G be its underlying graph. The adjacency rank of G ϕ , written as r ( G ϕ ) , is the rank of its adjacency matrix and denote by α ′ ( G ) the ...
Shuchao Li, Ting Yang
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Let G ϕ be an n-vertex complex unit gain graph and let G be its underlying graph. The adjacency rank of G ϕ , written as r ( G ϕ ) , is the rank of its adjacency matrix and denote by α ′ ( G ) the ...
Shuchao Li, Ting Yang
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The gap between the rank of a complex unit gain graph and its underlying graph
Discrete Applied MathematicszbMATH Open Web Interface contents unavailable due to conflicting licenses.
Du, Kexin, Lu, Yong, Zhou, Qiannan
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On -gain graphs with few positive eigenvalues
Linear and multilinear algebra, 2022Let $ \mathbb {T}_4=\{1,-1,\mathbf {i},-\mathbf {i}\} $ T4={1,−1,i,−i} be the group of fourth roots of unit. A $ \mathbb {T}_4 $ T4-gain graph is a graph where each orientation of an edge is given a complex unit in $ \mathbb {T}_4 $ T4, which is the ...
Xiaocong He, Lihua Feng, Lu Lu
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On the multiplicity of $A��$-eigenvalues and the rank of complex unit gain graphs
2021Let $ =(G, ) $ be a connected complex unit gain graph ($ \mathbb{T} $-gain graph) on a simple graph $ G $ with $ n $ vertices and maximum vertex degree $ $. The associated adjacency matrix and degree matrix are denoted by $ A( ) $ and $ D( ) $, respectively. Let $ m_ ( , ) $ be the multiplicity of $ $ as an eigenvalue of $ A_ ( ) := D(
Samanta, Aniruddha, Kannan, M. Rajesh
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