arXiv subjects

T. Sander

Publications and source records attributed to T. Sander.

3 recordsLinked to original sources

arXiv2012

Adding generators in cyclic groups

For a cyclic group $a$, define the atom of $a$ as the set of all elements generating $a$. Given any two elements $a,b$ of a finite cyclic group $G$, we study the sumset of the atom of $a$ and the atom of $b$. It is known that such a sumset is a disjoint union of atoms. The goal of this paper is to offer a deeper understanding of this phenomenon, by determining which atoms make up the sum of two given atoms and by computing the exact number of representations of each element of the sumset.

math.NT↗

arXiv2012

Distance Powers and Distance Matrices of Integral Cayley Graphs over Abelian Groups

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 of integral Cayley graphs over abelian groups have integral spectrum.

math.CO↗

arXiv2011

The exact maximal energy of integral circulant graphs with prime power order

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 graphs, also called gcd graphs, which can be characterized by their vertex count $n$ and a set $\cal D$ of divisors of $n$ in such a way that they have vertex set $\mathbb{Z}/n\mathbb{Z}$ and edge set $\{\{a,b\}:\, a,b\in\mathbb{Z}/n\mathbb{Z},\, \gcd(a-b,n)\in {\cal D}\}$. Given an arbitrary prime power $p^s$, we determine all divisor sets maximising the energy of an integral circulant graph of order $p^s$. This enables us to compute the maximal energy $\Emax{p^s}$ among all integral circulant graphs of order $p^s$.

math.CO↗