相关论文: Constructing graphs having Laplacian pair state tr…

In this article, we generate large families of non-isomorphic and signless Lalacian cospectral graphs using partial transpose on graphs. Our constructions are significantly powerful. More than $70\%$ of non-isomorphic signless-Laplacian…

The transfer of a quantum state between distant nodes in two-dimensional networks, is considered. The fidelity of state transfer is calculated as a function of the number of interactions in networks that are described by regular graphs. It…

It is not hard to find many complete bipartite graphs which are not determined by their spectra. We show that the graph obtained by deleting an edge from a complete bipartite graph is determined by its spectrum. We provide some graphs, each…

Typically, graph structures are represented by one of three different matrices: the adjacency matrix, the unnormalised and the normalised graph Laplacian matrices. The spectral (eigenvalue) properties of these different matrices are…

Half-arc-transitive graphs are a fascinating topic which connects graph theory, Riemann surfaces and group theory. Although fruitful results have been obtained over the last half a century, it is still challenging to construct…

Density matrices of graphs are combinatorial laplacians normalized to have trace one (Braunstein \emph{et al.} \emph{Phys. Rev. A,} \textbf{73}:1, 012320 (2006)). If the vertices of a graph are arranged as an array, then its density matrix…

Pairwise compatibility graphs (PCGs) with non-negative integer edge weights recently have been used to describe rare evolutionary events and scenarios with horizontal gene transfer. Here we consider the case that vertices are separated by…

In this study we consider the problem of triangulated graphs. Precisely we give a necessary and sufficient condition for a graph to be triangulated. This give an alternative characterization of triangulated graphs. Our method is based on…

We explore algebraic and spectral properties of weighted graphs containing twin vertices that are useful in quantum state transfer. We extend the notion of adjacency strong cospectrality to arbitrary Hermitian matrices, with focus on the…

This paper uses the theory of covering graphs to characterize some of the edge-transitive graphs which can arise as token graphs.

We consider the problem of constructing a bipartite graph whose degrees lie in prescribed intervals. Necessary and sufficient conditions for the existence of such graphs are well-known. However, existing realization algorithms suffer from…

Motivated by recent experiments and a theoretical analysis of the gap equation for the propagator of Dirac quasiparticles, we assume that the physics underlying the recently observed removal of sublattice and spin degeneracies in graphene…

The goal of this paper is to describe a sufficient condition on cycles in graphs for which the edge ideal is splittable. We give an explicit splitting function for such ideals.

Critical to the construction of large scale quantum networks, i.e. a quantum internet, is the development of fast algorithms for managing entanglement present in the network. One fundamental building block for a quantum internet is the…

It has long been known that there exist finite connected tetravalent arc-transitive graphs with arbitrarily large vertex-stabilisers. However, beside a well known family of exceptional graphs, related to the lexicographic product of a cycle…

Graphs can be associated with a matrix according to some rule and we can find the spectrum of a graph with respect to that matrix. Two graphs are cospectral if they have the same spectrum. Constructions of cospectral graphs help us…

A cycle in a graph is called dominating if every edge of the graph is incident with a vertex of the cycle. In this paper, we investigate forbidden pairs guaranteeing the existence of a dominating cycle in 2-connected graphs.

We discuss the question whether the existence of perfect matchings in a cubic graph can be seen from the spectrum of its adjacency matrix. For regular graphs in general and for three edge-disjoint perfect matchings in a cubic graph (that…

In this paper, we obtain a sufficient condition for the existence of parity factors in a regular graph in terms of edge-connectivity. Moreover, we also show that our condition is sharp.

This paper considers the problem of estimating high dimensional Laplacian constrained precision matrices by minimizing Stein's loss. We obtain a necessary and sufficient condition for existence of this estimator, that consists on checking…