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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 -gain graph is a triple consisting of an underlying graph , the circle group and a gain function , such that . In this paper, we focus our attention on the relations between the inertia indices of -gain graph Φ and the inertia indices of its underlying
Shahid Zaman, Xiaocong He
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Linear and multilinear algebra, 2020
Let be an n-vertex complex unit gain graph and let G be its underlying graph. The adjacency rank of , written as , is the rank of its adjacency matrix and denote by the matching number of the underlying graph G.
Shuchao Li, Ting Yang
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Let be an n-vertex complex unit gain graph and let G be its underlying graph. The adjacency rank of , written as , is the rank of its adjacency matrix and denote by the matching number of the underlying graph G.
Shuchao Li, Ting Yang
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Spectra of quaternion unit gain graphs
Linear Algebra and its Applications, 2022Abstract 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. +4 more
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Graph Neural Networks: Foundation, Frontiers and Applications
Knowledge Discovery and Data Mining, 2022The field of graph neural networks (GNNs) has seen rapid and incredible strides over the recent years. Graph neural networks, also known as deep learning on graphs, graph representation learning, or geometric deep learning, have become one of the fastest-
Lingfei Wu +4 more
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Decentralized Circular Formation Control of Nonholonomic Mobile Robots Under a Directed Sensor Graph
IEEE Transactions on Automatic Control, 2023This article investigates the circular formation control problem of multiple unicycle-type mobile robots under a directed sensor graph. The topology of the sensor graph among all robots is described by a directed graph containing a spanning tree, and the
Xiao Yu, R. Su
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GRAPHS DETERMINED BY THEIR -GAIN SPECTRA
Bulletin of the Australian Mathematical Society, 2020AbstractAn 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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Bipartite Consensus for Takagi-Sugeno Fuzzy Uncertain Multi-Agent Systems With Gain Fluctuations
IEEE Transactions on Signal and Information Processing over Networks, 2023This paper examines the problem of bipartite consensus for Takagi-Sugeno fuzzy multi-agent systems subject to uncertainties. The principal intention of this work is to develop a non-fragile controller through which the considered multi-agent system can ...
R. Sakthivel +3 more
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Graph Neural Networks: Foundation, Frontiers and Applications
Knowledge Discovery and Data Mining, 2023The field of graph neural networks (GNNs) has seen rapid and incredible strides over the recent years. Graph neural networks, also known as deep learning on graphs, graph representation learning, or geometric deep learning, have become one of the fastest-
Lingfei Wu +4 more
semanticscholar +1 more source