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The gamma-Signless Laplacian Adjacency Matrix of Mixed Graphs [PDF]

Theory and Applications of Graphs, 2023
The α-Hermitian adjacency matrix Hα of a mixed graph X has been recently introduced. It is a generalization of the adjacency matrix of unoriented graphs. In this paper, we consider a special case of the complex number α.
Omar Alomari, Mohammad Abudayah, Manal Ghanem   +2 more
doaj   +2 more sources

Hermitian-Randić matrix and Hermitian-Randić energy of mixed graphs

Journal of Inequalities and Applications, 2017
Let M be a mixed graph and H ( M ) $H(M)$ be its Hermitian-adjacency matrix. If we add a Randić weight to every edge and arc in M, then we can get a new weighted Hermitian-adjacency matrix. What are the properties of this new matrix?
Yong Lu, Ligong Wang, Qiannan Zhou
doaj   +2 more sources

Further Properties of Hermitian Adjacency Matrix of Mixed Graphs

Gulf Journal of Mathematics
The Hermitian adjacency matrix of a mixed graph extends the classical adjacency matrix to graphs containing both edges and arcs. In this paper, we establish a unified generalised interpretation for the powers of the Hermitian adjacency matrix, where arcs may be traversed in either direction and the orientation is encoded through complex conjugate ...
Yeni Susanti
exaly   +2 more sources

Hermitian adjacency matrix of the second kind for mixed graphs [PDF]

Discrete Mathematics, 2022
31pages ...
Shuchao Li, Yuantian Yu
openaire   +2 more sources

HS-integral and Eisenstein integral mixed circulant graphs

Theory and Applications of Graphs, 2023
A mixed graph is called \emph{second kind hermitian integral} (\emph{HS-integral}) if the eigenvalues of its Hermitian-adjacency matrix of the second kind are integers.
Monu Kadyan, Bikash Bhattacharjya
doaj   +1 more source

Hermitian Adjacency Matrix of Digraphs and Mixed Graphs [PDF]

Journal of Graph Theory, 2016
AbstractThe article gives a thorough introduction to spectra of digraphs via its Hermitian adjacency matrix. This matrix is indexed by the vertices of the digraph, and the entry corresponding to an arc from x to y is equal to the complex unity i (and its symmetric entry is ) if the reverse arc is not present.
Krystal Guo, Bojan Mohar
openaire   +2 more sources

Incidence matrices and line graphs of mixed graphs

Special Matrices, 2023
In the theory of line graphs of undirected graphs, there exists an important theorem linking the incidence matrix of the root graph to the adjacency matrix of its line graph. For directed or mixed graphs, however, there exists no analogous result.
Abudayah Mohammad, Alomari Omar, Sander Torsten   +2 more
doaj   +1 more source

Directed random geometric graphs: structural and spectral properties

Journal of Physics: Complexity, 2022
In this work we analyze structural and spectral properties of a model of directed random geometric graphs: given n vertices uniformly and independently distributed on the unit square, a directed edge is set between two vertices if their distance is ...
Kevin Peralta-Martinez, J A Méndez-Bermúdez   +1 more
doaj   +1 more source

Switching equivalence of Hermitian adjacency matrices of mixed graphs

, 2021
Let $0 \in Γ$ and $Γ\setminus \{0\}$ be a subgroup of the complex numbers of unit modulus. Define $\mathcal{H}_{n}(Γ)$ to be the set of all $n\times n$ Hermitian matrices with entries in $Γ$, whose diagonal entries are zero. The matrices $A,B\in \mathcal{H}_{n}(Γ)$ are said to be switching equivalent if there is a diagonal matrix $D$, in which the ...
Kadyan, Monu, Bhattacharjya, Bikash
openaire   +3 more sources

A new matrix representation of multidigraphs

AKCE International Journal of Graphs and Combinatorics, 2020
In this article, we introduce a new matrix associated with a multidigraph, named as the complex adjacency matrix. We study the spectral properties of bipartite multidigraphs corresponding to the complex adjacency matrix.
Sasmita Barik, Gopinath Sahoo
doaj   +1 more source