Related papers: Comparability digraphs: An analogue of comparabili…
Finding patterns in graphs is a fundamental problem in databases and data mining. In many applications, graphs are temporal and evolve over time, so we are interested in finding durable patterns, such as triangles and paths, which persist…
A D2CS of a graph G is a set $S \subseteq V(G)$ with $diam(G[S]) \leq 2$. We study the problem of counting and enumerating D2CS of a graph. First we give an explicit formula for the number of D2CS in a complete k-ary tree, Fibonacci tree,…
Let $G$ be a finite group and $N$ a normal subgroup of $G$. We determine the structure of $N$ when the graph $\Gamma_G(N)$, which is the graph associated to the conjugacy classes of $G$ contained in $N$, has no triangles and when the graph…
Link homotopy has been an active area of research for knot theorists since its introduction by Milnor in the 1950s. We introduce a new equivalence relation on spatial graphs called component homotopy, which reduces to link homotopy in the…
A large driver of the complexity of graph learning is the interplay between structure and features. When analyzing the expressivity of graph neural networks, however, existing approaches ignore features in favor of structure, making it…
Node classification and link prediction are widely studied in graph representation learning. While both transductive node classification and link prediction operate over a single input graph, they have so far been studied separately. Node…
We describe some metric properties of incomparability graphs. We consider the problem of the existence of infinite paths, either induced or isometric, in the incomparability graph of a poset. Among other things, we show that if the…
A perfect graph is a graph which every induced subgraph has clique number equal to chromatic number. In this paper, I will introduce a new family of graphs, the quasiperfect graphs which generalizes the perfect graphs.
In this article, we revisit and expand our prior work on graph similarity. As with our earlier work, we focus on a view of similarity which does not require node correspondence between graphs under comparison. Our work is suited to the…
Can neural networks learn to compare graphs without feature engineering? In this paper, we show that it is possible to learn representations for graph similarity with neither domain knowledge nor supervision (i.e.\ feature engineering or…
An imprimitive symmetric indecomposable association scheme of rank 5 is said to be Higmanian. A divisible design graph is a graph whose adjacency matrix is an incidence matrix of a symmetric divisible design. We establish conditions which…
Symmetry plays a major role in subgraph matching both in the description of the graphs in question and in how it confounds the search process. This work addresses how to quantify these effects and how to use symmetries to increase the…
We introduce the graph parameter readability and study it as a function of the number of vertices in a graph. Given a digraph D, an injective overlap labeling assigns a unique string to each vertex such that there is an arc from x to y if…
The restricted hypercube-like graphs, variants of the hypercube, were proposed as desired interconnection networks of parallel systems. The matching preclusion number of a graph is the minimum number of edges whose deletion results in the…
Graph Neural Networks have shown excellent performance on semi-supervised classification tasks. However, they assume access to a graph that may not be often available in practice. In the absence of any graph, constructing k-Nearest Neighbor…
A simple-triangle graph is the intersection graph of triangles that are defined by a point on a horizontal line and an interval on another horizontal line. The time complexity of the recognition problem for simple-triangle graphs was a…
Graphs have become increasingly popular in modeling structures and interactions in a wide variety of problems during the last decade. Graph-based clustering and semi-supervised classification techniques have shown impressive performance.…
Nested graphs have been used in different applications, for example to represent knowledge in semantic networks. On the other hand, graphs with cycles are really important in surface reconstruction, periodic schedule and network analysis.…
Subgraph Isomorphism uses a small graph as a pattern to identify within a larger graph a set of vertices that have matching edges. This paper addresses a logic program written in Prolog for a specific relatively complex graph pattern for…
In this paper we resolve the complexity of the isomorphism problem on all but finitely many of the graph classes characterized by two forbidden induced subgraphs. To this end we develop new techniques applicable for the structural and…