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We propose bipartite analogues of comparability and cocomparability graphs. Surprizingly, the two classes coincide. We call these bipartite graphs cocomparability bigraphs. We characterize cocomparability bigraphs in terms of vertex…

We introduce the Graph Mixture Density Networks, a new family of machine learning models that can fit multimodal output distributions conditioned on graphs of arbitrary topology. By combining ideas from mixture models and graph…

A mixed dominating set $S$ of a graph $G=(V,E)$ is a subset $ S \subseteq V \cup E$ such that each element $v\in (V \cup E) \setminus S$ is adjacent or incident to at least one element in $S$. The mixed domination number $\gamma_m(G)$ of a…

I investigate a class of dynamical systems in which finite pieces of spacetime contain finite amounts of information. Most of the guiding principles for designing these systems are drawn from general relativity: the systems are…

A graph is componentwise biconnected if every connected component either is an isolated vertex or is biconnected. We present a linear-time algorithm for the problem of adding the smallest number of edges to make a bipartite graph…

This paper proposes a novel representation of decomposable graphs based on semi-latent tree-dependent bipartite graphs. The novel representation has two main benefits. First, it enables a form of sub-clustering within maximal cliques of the…

We present a unified pipeline for univariate time series classification via complex networks and persistent homology. A time series is mapped to a graph through one of five constructions across three families (visibility (natural and…

A graph is an opposition graph, respectively, a coalition graph, if it admits an acyclic orientation which puts the two end-edges of every chordless 4-vertex path in opposition, respectively, in the same direction. Opposition and coalition…

In this article, we focus on the characteristic polynomial of a graph containingloops, but without multiple edges. We present a relationship between thecharacteristic polynomial of a graph with loops and the graph obtained byremoving all…

Characterisations of interval graphs, comparability graphs, co-comparability graphs, permutation graphs, and split graphs in terms of linear orderings of the vertex set are presented. As an application, it is proved that interval graphs,…

In this paper, we first present spectral conditions for the existence of $C_{n-1}$ in graphs (2-connected graphs) of order $n$, which are motivated by a conjecture of Erd\H{o}s. Then we prove spectral conditions for the existence of…

The control of bilinear systems has attracted considerable attention in the field of systems and control for decades, owing to their prevalence in diverse applications across science and engineering disciplines. Although much work has been…

Graph-based methods for signal processing have shown promise for the analysis of data exhibiting irregular structure, such as those found in social, transportation, and sensor networks. Yet, though these systems are often dynamic,…

For a given graph consider a pair of disjoint matchings the union of which contains as many edges as possible. Furthermore, consider the relation of the cardinalities of a maximum matching and the largest matching in those pairs. It is…

Stationarity is a cornerstone property that facilitates the analysis and processing of random signals in the time domain. Although time-varying signals are abundant in nature, in many practical scenarios the information of interest resides…

In this paper we give two characterisations of the class of reflexive graphs admitting distributive lattice polymorphisms and use these characterisations to address the problem of recognition: for a reflexive graph G in which no two…

We consider the algorithmic complexity of recognizing bipartite temporal graphs. Rather than defining these graphs solely by their underlying graph or individual layers, we define a bipartite temporal graph as one in which every layer can…

This paper considers a hyperplane arrangement constructed with a subset of a set of all simple paths in a graph. A connection of the constructed arrangement to the maximum matching problem is established. Moreover, the problem of finding…

In the recent years, several polynomial algorithms of a dynamical nature have been proposed to address the graph isomorphism problem. In this paper we propose a generalization of an approach exposed in cond-mat/0209112 and find that this…

Let $G=(V,E)$ be a simple graph without isolated vertices. A set $S\subseteq V$ is a paired-dominating set if every vertex in $V-S$ has at least one neighbor in $S$ and the subgraph induced by $S$ contains a perfect matching. In this paper,…