Results 231 to 240 of about 176,563 (257)

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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On the structure of matroids arising from the gain graphs

Discrete Mathematics, 2023
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Hamid Reza Maimani, Leila Parsaei-Majd, Mohammad Reza Pournaki, Milad Poursoltani   +3 more
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Inertia of complex unit gain graphs

Applied Mathematics and Computation, 2015
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Guihai Yu, Hui Qu, Jianhua Tu
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Spectra of quaternion unit gain graphs

Linear Algebra and its Applications, 2022
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Belardo F., Brunetti M., Coble N. J., Reff N., Skogman H.   +4 more
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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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Balance theory: an extension to conjugate skew gain graphs

2022
Summary: We extend the notion of balance from the realm of signed and gain graphs to conjugate skew gain graphs which are skew gain graphs where the labels on the oriented edges get conjugated when we reverse the orientation. We characterize the balance in a conjugate skew gain graph in several ways especially by dealing with its adjacency matrix and ...
Koombail, Shahul Hameed, K O, Ramakrishnan   +1 more
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Construction of cospectral graphs, signed graphs and $${\mathbb {T}}$$-gain graphs via partial transpose

Journal of Algebraic Combinatorics
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Belardo F., Brunetti M., Cavaleri M., Donno A.   +3 more
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On the wreath product of signed and gain graphs and its spectrum

Ars Mathematica Contemporanea
Summary: We introduce a notion of wreath product of two gain graphs \((\Gamma_1, \psi_1, G_1)\) and \((\Gamma_2, \psi_2, G_2)\), producing a gain graph over the direct product group \(G_2^{|V_{\Gamma_1}|} \times G_1\), whose underlying graph is the classical wreath product of graphs \(\Gamma_1 \wr \Gamma_2\).
Matteo Cavaleri, Alfredo Donno, Stefano Spessato   +2 more
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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, 2022
Shahid Zaman
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On the adjacency matrix of a complex unit gain graph

Linear and Multilinear Algebra, 2022
Rajesh Kannan M, Aniruddha Samanta, Ranjit Mehatari   +2 more
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