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We present an approach for reconstructing networks of pulse-coupled neuron-like oscillators from passive observation of pulse trains of all nodes. It is assumed that units are described by their phase response curves and that their phases…
The edge-hyper-Wiener index of a connected graph $G$ is defined as $WW_e(G) = \frac{1}{2}\sum_{\lbrace e,f\rbrace \subseteq E(G)}d(e,f) + \frac{1}{2}\sum_{\lbrace e,f\rbrace \subseteq E(G)}d(e,f)^2$. We develop a method for computing the…
For $k \ge 4$, let $Q_{2k}$ and $V_{2k}$ denote the ladder and M\"obius ladder on $2k$ vertices, respectively. We prove results that build on a result by Wormald that states that any cyclically $4$-connected cubic graph other than $Q_8$ or…
The chordal ring (CR) graphs are a well-known family of graphs used to model some interconnection networks for computer systems in which all nodes are in a cycle. Generalizing the CR graphs, in this paper, we introduce the families of…
We classify the planar cubic Cayley graphs of connectivity 2, providing an explicit presentation and embedding for each of them. Combined with [9] this yields a complete description of all planar cubic Cayley graphs.
The bandwidth of a graph is the labeling of vertices with minimum maximum edge difference. For many graph families this is NP-complete. A classic result computes the bandwidth for the hypercube. We generalize this result to give sharp lower…
Let $S$ be a set of vertices of a connected graph $G$. The Steiner distance of $S$ is the minimum size of a connected subgraph of $G$ containing all the vertices of $S$. The sum of all Steiner distances on sets of size $k$ is called the…
In recent years extensions of manifold Ricci curvature to discrete combinatorial objects such as graphs and hypergraphs (popularly called as "network shapes"), have found a plethora of applications in a wide spectrum of research areas…
In general graph theory, the only relationship between vertices are expressed via the edges. When the vertices are embedded in an Euclidean space, the geometric relationships between vertices and edges can be interesting objects of study.…
We define the entanglement-gradient routing scheme for quantum repeater networks. The routing framework fuses the fundamentals of swarm intelligence and quantum Shannon theory. Swarm intelligence provides nature-inspired solutions for…
This paper focuses on the embeddability of hypercubes in an important class of Cayley graphs, known as augmented cubes. An $n$-dimensional augmented cube $AQ_n$ is constructed by augmenting the $n$-dimensional hypercube $Q_n$ with…
We study the properties of discrete-time random walks on networks formed by randomly interconnected cliques, namely, random networks of cliques. Our purpose is to derive the parameters that define the network structure -- specifically, the…
Acyclic networks are a class of complex networks in which links are directed and don't have closed loops. Here we present an algorithm for transforming an ordinary undirected complex network into an acyclic one. Further analysis of an…
A measure for the maximum quantum information transfer capacity (ITC) between nodes of a spin network is defined, and shown to induce a metric on a space of equivalence classes of nodes for homogeneous chains with XX and Heisenberg…
In this paper, the branches of recursive and recurrent neural networks are classified in detail according to the network structure, training objective function and learning algorithm implementation. They are roughly divided into three…
Complex networks can be used to represent and model an ample diversity of abstract and real-world systems and structures. A good deal of the research on these structures has focused on specific topological properties, including node degree,…
Periodic orbits (equivalence classes of closed paths up to cyclic shifts) play an important role in applications of graph theory. For example, they appear in the definition of the Ihara zeta function and exact trace formulae for the spectra…
We propose the theory of Cayley graphs as a framework to analyse gate counts and quantum costs resulting from reversible circuit synthesis. Several methods have been proposed in the reversible logic synthesis literature by considering…
We classify certain non-symmetric commutative association schemes. As an application, we determine all the weakly distance-regular circulants of one type of arcs by using Schur rings. We also give the classification of primitive weakly…
This paper studies reduced-order modeling of dynamic networks with strongly connected topology. Given a graph clustering of an original complex network, we construct a quotient graph with less number of vertices, where the edge weights are…