Related papers: Fibonacci-run graphs I: basic properties

Network topology is a fundamental aspect of network science that allows us to gather insights into the complicated relational architectures of the world we inhabit. We provide a first specific study of neighbourhood degree sequences in…

The class of quasi-chain graphs is an extension of the well-studied class of chain graphs. This latter class enjoys many nice and important properties, such as bounded clique-width, implicit representation, well-quasi-ordering by induced…

As data structures and mathematical objects used for complex systems modeling, hypergraphs sit nicely poised between on the one hand the world of network models, and on the other that of higher-order mathematical abstractions from algebra,…

By investigating a recurrence relation about functions, we first give alternative proofs of various identities on Fibonacci numbers and Lucas numbers, and then, make certain well known identities visible via certain trivalent graph…

In this paper we consider two natural notions of connectivity for hypergraphs: weak and strong. We prove that the strong vertex connectivity of a connected hypergraph is bounded by its weak edge connectivity, thereby extending a theorem of…

Recurrent Neural Networks (RNNs) have been proven to be effective in modeling sequential data and they have been applied to boost a variety of tasks such as document classification, speech recognition and machine translation. Most of…

In this paper, we define the bi-periodic Fibonacci matrix sequence that represent bi-periodic Fibonacci numbers. Then, we investigate generating function, Binet formula and summations of bi-periodic Fibonacci matrix sequence. After that, we…

We introduce a novel definition of curvature for hypergraphs, a natural generalization of graphs, by introducing a multi-marginal optimal transport problem for a naturally defined random walk on the hypergraph. This curvature, termed…

We collect some general results on graph limits associated to hereditary classes of graphs. As examples, we consider some classes defined by forbidden subgraphs and some classes of intersection graphs, including triangle-free graphs,…

Biological and cellular systems are often modeled as graphs in which vertices represent objects of interest (genes, proteins, drugs) and edges represent relational ties among these objects (binds-to, interacts-with, regulates). This…

In many networks, vertices have hidden attributes, or types, that are correlated with the networks topology. If the topology is known but these attributes are not, and if learning the attributes is costly, we need a method for choosing…

We investigate which graphs H have the property that in every graph with bounded clique number and sufficiently large chromatic number, some induced subgraph is isomorphic to a subdivision of H. In an earlier paper, one of us proved that…

A graph is circle if its vertices are in correspondence with a family of chords in a circle in such a way that every two distinct vertices are adjacent if and only if the corresponding chords have nonempty intersection. Even though there…

In descending generality I survey: five partial orderings of graphs, the induced-subgraph ordering, and examples like perfect, threshold, and mock threshold graphs. The emphasis is on how the induced subgraph ordering differs from other…

This article describes an approach to modeling knowledge acquisition in terms of walks along complex networks. Each subset of knowledge is represented as a node, and relations between such knowledge are expressed as edges. Two types of…

The cut sets of a graph are special sets of vertices whose removal disconnects the graph. They are fundamental in the study of binomial edge ideals, since they encode their minimal primary decomposition. We introduce the class of accessible…

Here in particular, we give a characterization of Quasi-line Graphs in terms of forbidden induced subgraphs. In general, we prove a necessary and sufficient condition for a graph to be a union of two cliques.

In the first part of this work we provide a formula for the number of edges of the Hasse diagram of the independent subsets of the h-th power of a path ordered by inclusion. For h=1 such a value is the number of edges of a Fibonacci cube.…

Across the sciences, the statistical analysis of networks is central to the production of knowledge on relational phenomena. Because of their ability to model the structural generation of networks, exponential random graph models are a…

Discrete curvatures are quantities associated to the nodes and edges of a graph that reflect the local geometry around them. These curvatures have a rich mathematical theory and they have recently found success as a tool to analyze networks…