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, which is the inverse of the quaternion unit assigned to the opposite …

Abstract Let Φ=(G, φ) be a connected complex unit gain graph (T-gain graph) of n vertices
with largest vertex degree Δ, adjacency matrix A (Φ), and degree matrix D (Φ). Let m α (Φ, λ) …

A complex unit gain graph (or $\mathbb T $-gain graph) is a gain graph with gains in
$\mathbb T $, the multiplicative group of complex units. Extending a classical construction …

This article gives some fundamental introduction to spectra of mixed graphs via its k-
generalized Hermitian adjacency matrix. This matrix is indexed by the vertices of the mixed …

A complex unit gain graph is a graph where each orientation of an edge is given a complex
unit, which is the inverse of the complex unit assigned to the opposite orientation. In this …

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 …

Abstract Let Φ=(G, φ) be a T-gain graph with maximum degree Δ. Zhou et al.(2018)[35] gave
a lower bound of the rank of simple graphs in items of maximum degree. Motivated by above …

Abstract Let Φ=(Γ, φ) be a T-gain graph or a complex unit gain graph and A (Φ) be its
adjacency matrix. The rank of (Γ, φ) is denoted by r (Γ, φ) which is the rank of its adjacency …

Abstract Let Φ=(G, φ) be a complex unit gain graph (or T-gain graph) and A (Φ) be its
adjacency matrix, where G is the underlying graph of Φ. The rank r (Φ) of Φ is the rank of A …