Related papers: Maximal Pivots on Graphs with an Application to Ge…
Graph kernels are widely used for measuring the similarity between graphs. Many existing graph kernels, which focus on local patterns within graphs rather than their global properties, suffer from significant structure information loss when…
Causal graph dynamics are transformations over graphs that capture two important symmetries of physics, namely causality and homogeneity. They can be equivalently defined as continuous and translation invariant transformations or functions…
We study the problem of finding the minimal (maximal) genus for a surface where a given four-valent graph with fixed opposite edge structure can be embedded into. We find several partial relations and give new reformulations in…
In this report, we describe a novel graph invariant for computational graphs (colored directed acylic graphs) and how we used it to generate all distinct computational graphs up to isomorphism for small graphs. The algorithm iteratively…
Learning generative models for graph-structured data is challenging because graphs are discrete, combinatorial, and the underlying data distribution is invariant to the ordering of nodes. However, most of the existing generative models for…
We examine the Maximum Independent Set Problem in an undirected graph. The main result is that this problem can be considered as the solving the same problem in a subclass of the weighted normal twin-orthogonal graphs. The problem is…
The mincut graph bisection problem involves partitioning the n vertices of a graph into disjoint subsets, each containing exactly n/2 vertices, while minimizing the number of "cut" edges with an endpoint in each subset. When considered over…
Fractional revival is a quantum transport phenomenon important for entanglement generation in spin networks. This takes place whenever a continuous-time quantum walk maps the characteristic vector of a vertex to a superposition of the…
Random graphs are more and more used for modeling real world networks such as evolutionary networks of proteins. For this purpose we look at two different models and analyze how properties like connectedness and degree distributions are…
The pathway is a biological term that refers to a series of interactions between molecules in a cell that causes a certain product or a change in the cell. Pathway analysis is a powerful method for gene expression analysis. Through pathway…
A graph $G$ is said to be a `set graph' if it admits an acyclic orientation that is also `extensional', in the sense that the out-neighborhoods of its vertices are pairwise distinct. Equivalently, a set graph is the underlying graph of the…
Given an oriented graph $D$, the inversion of a subset $X$ of vertices consists in reversing the orientation of all arcs with both endpoints in $X$. When the subset $X$ is of size $p$ (resp. at most $p$), this operation is called an…
Vertex splitting replaces a vertex by two copies and partitions its incident edges amongst the copies. This problem has been studied as a graph editing operation to achieve desired properties with as few splits as possible, most often…
We consider the constrained graph alignment problem which has applications in biological network analysis. Given two input graphs $G_1=(V_1,E_1), G_2=(V_2,E_2)$, a pair of vertex mappings induces an {\it edge conservation} if the vertex…
Given an underlying undirected simple graph, we consider the set of all acyclic orientations of its edges. Each of these orientations induces a partial order on the vertices of our graph and, therefore, we can count the number of linear…
In this paper extremal values of the difference between several graph invariants related to the metric dimension are studied: mixed metric dimension, edge metric dimension and strong metric dimension. These non-trivial extremal values are…
The family of mappings of the plane possessing a biquadratic invariant, which is known collectively as QRT maps, is composed of two involutions, one preserving a vertical shift and the other preserving a horizontal shift in the plane. In…
We consider the maintenance of maximal bicliques from a dynamic bipartite graph that changes over time due to the addition or deletion of edges. When the set of edges in a graph changes, we are interested in knowing the change in the set of…
Horizontal gene transfer is an important contributor to evolution. According to Walter M.\ Fitch, two genes are xenologs if they are separated by at least one HGT. More formally, the directed Fitch graph has a set of genes is its vertices,…
In an oriented graph $\overrightarrow{G}$, the inversion of a subset $X$ of vertices is the operation that reverses the orientation of all arcs with both end-vertices in $X$. The inversion graph of a graph $G$, denoted by $\mathcal{I}(G)$,…