We propose a supplement matrix method for computing eigenvalues of a dual Hermitian
matrix and discuss its application in multiagent formation control. Suppose we have a ring …

In 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 …

A quaternion unit gain graph is a graph where each orientation of an edge is given a
quaternion unit, and the opposite orientation is assigned the inverse of this quaternion unit …

The paper presents the original structure of a processing unit for multiplying quaternions.
The idea of organizing the device is based on the use of fast Hadamard transform blocks …

In this paper, we study dual complex unit gain graphs and their spectral properties. We
establish the interlacing theorem for dual complex unit gain graphs, and show that the …

We define G-cospectrality of two G-gain graphs (Γ, ψ) and (Γ′, ψ′), proving that it is a
switching isomorphism invariant. When G is a finite group, we prove that G-cospectrality is …

A gain graph over a group G, also referred to as G-gain graph, is a graph where an element
of a group G, called gain, is assigned to each oriented edge, in such a way that the inverse …

We 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 …

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 …

We introduce a definition for the total graph of a gain graph (Γ, ψ) on a group G by using G-
phases, which are a generalization of the notion of orientation to gain graphs. Our …