21 citations · 73 across the 9 of their papers we have counts for
10 papers
Incidence matrices and line graphs of mixed graphs
Mohammad Abudayah, Omar Alomari, Torsten Sander
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 di…
Hermitian Adjacency Matrices of Mixed Graphs
Mohammad Abudayah, Omar Alomari, Torsten Sander
The traditional adjacency matrix of a mixed graph is not symmetric in general, hence its eigenvalues may be not real. To overcome this obstacle, several authors have recently defin…
Spectrum of free-form Sudoku graphs
Mohammad Abudayah, Omar Alomari, Torsten Sander
A free-form Sudoku puzzle is a square arrangement of m times m cells such that the cells are partitioned into m subsets (called blocks) of equal cardinality. The goal of the puzzle…
Adding generators in cyclic groups
J. W. Sander, T. Sander
For a cyclic group , define the atom of as the set of all elements generating . Given any two elements of a finite cyclic group , we study the sumset of the atom…
Distance Powers and Distance Matrices of Integral Cayley Graphs over Abelian Groups
W. Klotz, T. Sander
It is shown that distance powers of an integral Cayley graph over an abelian group are again integral Cayley graphs over that group. Moreover, it is proved that distance matrices o…
The maximal energy of classes of integral circulant graphs
Jürgen W. Sander, Torsten Sander
The energy of a graph is the sum of the moduli of the eigenvalues of its adjacency matrix. We study the energy of integral circulant graphs, also called gcd graphs, which can be ch…
Integral circulant graphs of prime power order with maximal energy
Jürgen W. Sander, Torsten Sander
The energy of a graph is the sum of the moduli of the eigenvalues of its adjacency matrix. We study the energy of integral circulant graphs, also called gcd graphs, which can be ch…
On the eigenvalues of distance powers of circuits
Jürgen W. Sander, Torsten Sander
Taking the d-th distance power of a graph, one adds edges between all pairs of vertices of that graph whose distance is at most d. It is shown that only the numbers -3, -2, -1, 0,…
Tree Decomposition By Eigenvectors
Torsten Sander, Jürgen W. Sander
In this work a composition-decomposition technique is presented that correlates tree eigenvectors with certain eigenvectors of an associated so-called skeleton forest. In particula…
The exact maximal energy of integral circulant graphs with prime power order
J. W. Sander, T. Sander
The energy of a graph was introduced by {\sc Gutman} in 1978 as the sum of the absolute values of the eigenvalues of its adjacency matrix. We study the energy of integral circulant…