Results 11 to 20 of about 180,088 (293)
Normalized Laplacians for gain graphs [PDF]
The American Journal of Combinatorics, 2022 We propose the notion of normalized Laplacian matrix $\mathcal{L}(\Phi)$ for a gain graph $\Phi$ and study its properties in detail, providing insights and counterexamples along the way.
M. Rajesh Kannan +2 more
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Line and Subdivision Graphs Determined by
Mathematics, 2019 Let T 4 = { ± 1 , ± i } be the subgroup of fourth roots of unity inside T , the multiplicative group of complex units. For a T 4 -gain graph Φ = ( Γ , T 4 , φ ) , we introduce gain functions on ...
Abdullah Alazemi +4 more
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Coloring permutation-gain graphs
Contributions to Discrete Mathematics, 2021 Correspondence colorings of graphs were introduced in 2018 by Dvořák and Postle as a generalization of list colorings of graphs which generalizes ordinary graph coloring.
Slilaty, Daniel
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Balance in gain graphs – A spectral analysis
Linear Algebra and its Applications, 2012 A gain graph is a graph 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.
Germina, K.A. +3 more
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Characterizations of line graphs in signed and gain graphs [PDF]
European Journal of Combinatorics, 2022 We generalize three classical characterizations of line graphs to line graphs of signed and gain graphs: the Krausz's characterization, the van Rooij and Wilf's characterization and the Beineke's characterization. In particular, we present a list of forbidden gain subgraphs characterizing the class of gain-line graphs.
Matteo Cavaleri +2 more
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Gain distance matrices for complex unit gain graphs
Discrete Mathematics, 2022 20 pages; 2 ...
Aniruddha Samanta, M. Rajesh Kannan
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Spectral Properties of Dual Unit Gain Graphs
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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Matroids of Gain Signed Graphs
Discrete & Computational Geometry, 2023 13 fig., 46 pp. v2 has new Example 3.7, minor editing, 47 pp.
Laura Anderson +2 more
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Gain distance Laplacian matrices for complex unit gain graphs
A complex unit gain graph (or a $\mathbb{T}$-gain graph) $\Theta(\Sigma,\varphi)$ is a graph where the unit complex number is assign by a function $\varphi$ to every oriented edge of $\Sigma$ and assign its inverse to the opposite orientation.
Khan, Suliman
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A Matrix Approach for Analyzing Signal Flow Graph
Information, 2020 Mason’s gain formula can grow factorially because of growth in the enumeration of paths in a directed graph. Each of the (n − 2)! permutation of the intermediate vertices includes a path between input and output nodes.
Shyr-Long Jeng +2 more
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