相关论文: One more proof about the spectrum of Transposition…
We show that the directed labelled Cayley graphs coincide with the rooted deterministic vertex-transitive simple graphs. The Cayley graphs are also the strongly connected deterministic simple graphs of which all vertices have the same cycle…
We use the line digraph construction to associate an orthogonal matrix with each graph. From this orthogonal matrix, we derive two further matrices. The spectrum of each of these three matrices is considered as a graph invariant. For the…
A graph $\Gamma$ is $G$-symmetric if it admits $G$ as a group of automorphisms acting transitively on the set of arcs of $\Gamma$, where an arc is an ordered pair of adjacent vertices. Let $\Gamma$ be a $G$-symmetric graph such that its…
A complex unit gain graph is a simple graph in which each orientation of an edge is given a complex number with modulus 1 and its inverse is assigned to the opposite orientation of the edge. In this article, first we establish bounds for…
We study the symmetry properties of the spectra of normalized Laplacians on signed graphs. We find a new machinery that generates symmetric spectra for signed graphs, which includes bipartiteness of unsigned graphs as a special case.…
We define super-Cayley graphs over a finite abelian group $G$. Using the theory of supercharacters on $G$, we explain how their spectra can be realized as a super-Fourier transform of a superclass characteristic function. Consequently, we…
Whitney's Broken-cycle Theorem states the chromatic polynomial of a graph as a sum over special edge subsets. We give a definition of cycles in hypergraphs that preserves the statement of the theorem there.
We initiate the study of Hamiltonian cycles up to symmetries of the underlying graph. Our focus lies on the extremal case of Hamiltonian-transitive graphs, i.e., Hamiltonian graphs where, for every pair of Hamiltonian cycles, there is a…
A general framework is presented which unifies the treatment of wavelet-like, quasidistribution, and tomographic transforms. Explicit formulas relating the three types of transforms are obtained. The case of transforms associated to the…
For a group $G$ and subsets $S,T \subset G$ we introduce the mirror di-Cayley graph $MX(G;S,T)$ and mirror di-Cayley sum graph $MX^+(G;S,T)$ with connections sets $S$ and $T$ (MDCGs for short). We refer to them indistinctly by…
We study the spectrum of the join of several circulant matrices. We apply our results to compute explicitly the spectrum of certain graphs obtained by joining several circulant graphs.
According to the O'Nan--Scott Theorem, a finite primitive permutation group either preserves a structure of one of three types (affine space, Cartesian lattice, or diagonal semilattice), or is almost simple. However, diagonal groups are a…
An arbitrary Feynman graph for string field theory interactions is analysed and the homeomorphism type of the corresponding world sheet surface is completely determined even in the non-orientable cases. Algorithms are found to mechanically…
Let M be a module over a commutative ring and let Spec(M) (resp. Max(M)) be the collection of all prime (resp. maximal) submodules of M. We topologize Spec(M) with Zariski topology, which is analogous to that for Spec(R), and consider…
Resolving parameters is a fundamental area of combinatorics with applications not only to many branches of combinatorics but also to other sciences. In this article, we construct a class of Toeplitz graphs, and will be denoted by…
Let $\Gamma$ be a graph and let $G$ be a group of automorphisms of $\Gamma$. The graph $\Gamma$ is called $G$-normal if $G$ is normal in the automorphism group of $\Gamma$. Let $T$ be a finite non-abelian simple group and let $G = T^l$ with…
In this paper we introduce a Cayley-type graph for group-subgroup pairs and present some elementary properties of such graphs, including connectedness, their degree and partition structure, and vertex-transitivity. We relate these…
A permutation graph is a graph that can be derived from a permutation, where the vertices correspond to letters of the permutation, and the edges represent inversions. We provide a construction to show that there are infinitely many…
We study the transmission of a quantum particle along a straight input--output line to which a graph $\Gamma$ is attached at a point. In the point of contact we impose a singularity represented by a certain properly chosen scale-invariant…
Arrangement graphs were introduced for their connection to computational networks and have since generated considerable interest in the literature. In a pair of recent articles by Chen, Ghorbani and Wong, the eigenvalues for the adjacency…