Related papers: Self-testing graph states
Random intersection graphs model networks with communities, assuming an underlying bipartite structure of groups and individuals, where these groups may overlap. Group memberships are generated through the bipartite configuration model.…
In this paper, we use the concept of colored edge graphs to model homogeneous faults in networks. We then use this model to study the minimum connectivity (and design) requirements of networks for being robust against homogeneous faults…
The entanglement of graph states up to eight qubits is calculated in the regime of iteration calculation. The entanglement measures could be the relative entropy of entanglement, the logarithmic robustness or the geometric measure. All 146…
Graph states and hypergraph states are of wide interest in quantum information processing and foundational studies. Efficient verification of these states is a key to various applications. Here we propose a simple method for verifying…
We characterize stability of graph C*-algebras by giving five conditions equivalent to their stability. We also show that if G is a graph with no sources, then C*(G) is stable if and only if each vertex in G can be reached by an infinite…
We study the problem of testing for community structure in networks using relations between the observed frequencies of small subgraphs. We propose a simple test for the existence of communities based only on the frequencies of three-node…
We show that if a graph $G$ satisfies certain conditions then the connectivity of neighbourhood complex $\mathcal{N}(G)$ is strictly less than the vertex connectivity of $G$. As an application, we give a relation between the connectivity of…
In the past two decades, significant advances have been made in understanding the structural and functional properties of biological networks, via graph-theoretic analysis. In general, most graph-theoretic studies are conducted in the…
In an earlier paper the authors proved that limits of convergent graph sequences can be described by various structures, including certain 2-variable real functions called graphons, random graph models satisfying certain consistency…
For many graph-related problems, it can be essential to have a set of structurally diverse graphs. For instance, such graphs can be used for testing graph algorithms or their neural approximations. However, to the best of our knowledge, the…
Testing a graph on 2-vertex- and 2-edge-connectivity are two fundamental algorithmic graph problems. For both problems, different linear-time algorithms with simple implementations are known. Here, an even simpler linear-time algorithm is…
Do algorithms for drawing graphs pass the Turing Test? That is, are their outputs indistinguishable from graphs drawn by humans? We address this question through a human-centred experiment, focusing on `small' graphs, of a size for which it…
In this article we consider resistance matrix of a connected graph. For unweighted graph we study some necessary and sufficient conditions for resistance regular graphs. Also we find some relationship between Laplacian matrix and resistance…
We present a general method to characterize the quantum correlations obtained after local measurements on multipartite systems. Sufficient conditions for a quantum system to be fully-nonlocal according to a given partition, as well as being…
The name graph state is used to describe a certain class of pure quantum state which models a physical structure on which one can perform measurement-based quantum computing, and which has a natural graphical description. We present the…
In order to apply canonical labelling of graphs and isomorphism checking in interactive theorem provers, these checking algorithms must either be mechanically verified or their results must be verifiable by independent checkers. We analyze…
Let ${\mathcal G}$ be an infinite family of connected graphs and let $k$ be a positive integer. We say that $k$ is ${\it forcing}$ for ${\mathcal G}$ if for all $G \in {\mathcal G}$ but finitely many, the following holds. Any…
A random intersection graph is constructed by independently assigning a subset of a given set of objects $W,$ to each vertex of the vertex set $V$ of a simple graph $G.$ There is an edge between two vertices of $V,$ iff their respective…
We give a sharp bound for the automorphism group of a cubic simple graph with a given number of vertices. For each number of vertices we give an explicit graph attaining the bound, and prove its uniqueness in special cases.
For a given multigraph H, a graph G is H-linked, if |G| \geq |H| and for every injective map {\tau}: V (H) \rightarrow V (G), we can find internally disjoint paths in G, such that every edge from uv in H corresponds to a {\tau} (u) - {\tau}…