Related papers: What Graphs are 2-Dot Product Graphs?
Graph representation plays an important role in the field of financial risk control, where the relationship among users can be constructed in a graph manner. In practical scenarios, the relationships between nodes in risk control tasks are…
Let $P$ be a set of $n\geq 3$ points in general position in the plane. The edge disjointness graph $D(P)$ of $P$ is the graph whose vertices are all the closed straight line segments with endpoints in $P$, two of which are adjacent in…
In this paper, we explore the concept of the ``matrix product of graphs," initially introduced by Prasad, Sudhakara, Sujatha, and M. Vinay. This operation involves the multiplication of adjacency matrices of two graphs with assigned labels,…
In this paper we investigate the connectedness and the isomorphism problems for zig-zag products of two graphs. A sufficient condition for the zig-zag product of two graphs to be connected is provided, reducing to the study of the…
In this article, we extend several algebraic graph analysis methods to bipartite networks. In various areas of science, engineering and commerce, many types of information can be represented as networks, and thus the discipline of network…
We study characteristics which might distinguish two-graphs by introducing different numerical measures on the collection of graphs on $n$ vertices. Two conjectures are stated, one using these numerical measures and the other using the deck…
Graphs are a useful abstraction of image content. Not only can graphs represent details about individual objects in a scene but they can capture the interactions between pairs of objects. We present a method for training a convolutional…
Let $G=(V,E)$ be a connected graph, let $v\in V$ be a vertex and let $e=uw\in E$ be an edge. The distance between the vertex $v$ and the edge $e$ is given by $d_G(e,v)=\min\{d_G(u,v),d_G(w,v)\}$. A vertex $w\in V$ distinguishes two edges…
The distinguishing number $D(G)$ of a graph $G$ is the least integer $d$ such that $G$ has a vertex labeling with $d$ labels that is preserved only by a trivial automorphism. We say that a graph $G$ is $d$-distinguishing critical, if…
It was recently proved that every planar graph is a subgraph of the strong product of a path and a graph with bounded treewidth. This paper surveys generalisations of this result for graphs on surfaces, minor-closed classes, various…
A graph $G$ of order $2n$ is called degree-equipartite if for every $n$-element set $A\subseteq V(G)$, the degree sequences of the induced subgraphs $G[A]$ and $G[V(G)\setminus A]$ are the same. In this paper, we characterize all…
A $k$-regular graph is called a divisible design graph (DDG for short) if its vertex set can be partitioned into $m$ classes of size $n$, such that two distinct vertices from the same class have exactly $\lambda_1$ common neighbors, and two…
Models of complex networks are generally defined as graph stochastic processes in which edges and vertices are added or deleted over time to simulate the evolution of networks. Here, we define a unifying framework - probabilistic inductive…
We adapt the classical 3-decomposition of any 2-connected graph to the case of simple graphs (no loops or multiple edges). By analogy with the block-cutpoint tree of a connected graph, we deduce from this decomposition a bicolored tree…
Graphs arise naturally in many real-world applications including social networks, recommender systems, ontologies, biology, and computational finance. Traditionally, machine learning models for graphs have been mostly designed for static…
This paper considers the edge-connectivity and restricted edge-connectivity of replacement product graphs, gives some bounds on edge-connectivity and restricted edge-connectivity of replacement product graphs and determines the exact values…
Graph matching aims to establish correspondences between vertices of graphs such that both the node and edge attributes agree. Various learning-based methods were recently proposed for finding correspondences between image key points based…
We investigate the joint distribution of the vertex degrees in three models of random bipartite graphs. Namely, we can choose each edge with a specified probability, choose a specified number of edges, or specify the vertex degrees in one…
In this work, we define an orthogonal graph on the set of equivalence classes of $(2\nu + \delta)-$tuples over $\mathbb{Z}_{2^n}$ where $n$ and $\nu$ are positive integers and $\delta = 0, 1$ or $2$. We classify our graph if it is strongly…
For networks of coupled dynamical systems we characterize admissible functions, that is, functions whose gradient is an admissible vector field. The schematic representation of a gradient network dynamical system is of an undirected cell…