Related papers: on removal of perfect matching from folded hypercu…
Shared entanglement can significantly amplify classical correlations between systems interacting over a limited quantum channel. A natural avenue is to use entanglement of the same dimension as the channel because this allows for unitary…
A complete characterization and quantification of entanglement, particularly the multipartite entanglement, remains an unfinished long-term goal in quantum information theory. As long as the multipartite system is concerned, the relation…
This paper considers a kind of generalized measure $\lambda_s^{(h)}$ of fault tolerance in a hypercube-like graph $G_n$ which contain several well-known interconnection networks such as hypercubes, varietal hypercubes, twisted cubes,…
We introduce, and partially resolve, a conjecture that brings a three-centuries-old derangements phenomenon and its much younger two-decades-old analogue under the same umbrella. Through a graph-theoretic lens, a derangement is a perfect…
The linear finite irreducible representations of the algebra of the 1D $N$-Extended Supersymmetric Quantum Mechanics are discussed in terms of their "connectivity" (a symbol encoding information on the graphs associated to the irreps). The…
The set of all subspaces of $\mathbb{F}_q^n$ is denoted by $\mathbb{P}_q(n)$. The subspace distance $d_S(X,Y) = \dim(X)+ \dim(Y) - 2\dim(X \cap Y)$ defined on $\mathbb{P}_q(n)$ turns it into a natural coding space for error correction in…
Structure connectivity and substructure connectivity are innovative indicators for assessing network reliability and fault tolerance. Similarly, fault diameter evaluates fault tolerance and transmission delays in networks. This paper…
We study separating matchings in graphs, that is, matchings whose removal increases the number of connected components, and focus on determining the maximum size of such a matching in a graph $G$, denoted by $\mathrm{mms}(G)$. We show that…
Twisted hypercube-like networks (THLNs) are an important class of interconnection networks for parallel computing systems, which include most popular variants of the hypercubes, such as crossed cubes, M\"obius cubes, twisted cubes and…
Szepietowski [A. Szepietowski, Hamiltonian cycles in hypercubes with $2n-4$ faulty edges, Information Sciences, 215 (2012) 75--82] observed that the hypercube $Q_n$ is not Hamiltonian if it contains a trap disconnected halfway. A proper…
Suppose that there exists a discrete subset $X$ of a complete, connected, $n$-dimensional Riemannian manifold $M$ such that the Riemannian distances between points of $X$ correspond to the Euclidean distances of a net in $\mathbb{R}^{n}$.…
Let $\mathbb{F}_q$ be a finite field. Given two irreducible polynomials $f,g$ over $\mathbb{F}_q$, with $\mathrm{deg} f$ dividing $\mathrm{deg} g$, the finite field embedding problem asks to compute an explicit description of a field…
A graph $G$ is {\em matching-decyclable} if it has a matching $M$ such that $G-M$ is acyclic. Deciding whether $G$ is matching-decyclable is an NP-complete problem even if $G$ is 2-connected, planar, and subcubic. In this work we present…
It has been conjectured that whenever an optimal covering array exists there is also a uniform covering array with the same parameters and this is true for all known optimal covering arrays. When used as a test suite, the application…
A particularly simple description of separability of quantum states arises naturally in the setting of complex algebraic geometry, via the Segre embedding. This is a map describing how to take products of projective Hilbert spaces. In this…
Let $V$ denote an $r$-dimensional $\mathbb{F}_{q^n}$-vector space. For an $m$-dimensional $\mathbb{F}_q$-subspace $U$ of $V$ assume that $\dim_q \left(\langle {\bf v}\rangle_{\mathbb{F}_{q^n}} \cap U\right) \geq 2$ for each non zero vector…
The perfect matching complex of a simple graph $G$ is a simplicial complex having facets (maximal faces) as the perfect matchings of $G$. This article discusses the perfect matching complex of polygonal line tilings and the $\left(2 \times…
A matching $M$ in a graph $G$ is uniquely restricted if no other matching in $G$ covers the same set of vertices. We conjecture that every connected subcubic graph with $m$ edges and $b$ bridges that is distinct from $K_{3,3}$ has a…
Geometric deep learning enables the encoding of physical symmetries in modeling 3D objects. Despite rapid progress in encoding 3D symmetries into Graph Neural Networks (GNNs), a comprehensive evaluation of the expressiveness of these…
Superconducting quantum circuits, fabricated with multiple layers, are proposed to implement perfect quantum state transfer between nodes of a hypercube network. For tunable devices such as the phase qubit, each node can transmit quantum…