Related papers: SuperNOVA: a novel algorithm for graph automorphis…
Any finite group can be encoded as the automorphism group of an unlabeled simple graph. Recently Hartke, Kolb, Nishikawa, and Stolee (2010) demonstrated a construction that allows any ordered pair of finite groups to be represented as the…
Graph clustering is the problem of identifying sparsely connected dense subgraphs (clusters) in a given graph. Proposed clustering algorithms usually optimize various fitness functions that measure the quality of a cluster within the graph.…
By a map we mean a $2$-cell decomposition of a closed compact surface, i.e., an embedding of a graph such that every face is homeomorphic to an open disc. Automorphism of a map can be thought of as a permutation of the vertices which…
We examine ordered graphs, defined as graphs with linearly ordered vertices, from the perspective of homomorphisms (and colorings) and their complexities. We demonstrate the corresponding computational and parameterized complexities, along…
The use of graph neural networks has produced significant advances in point cloud problems, such as those found in high energy physics. The question of how to produce a graph structure in these problems is usually treated as a matter of…
Graph isomorphism, a classical algorithmic problem, determines whether two input graphs are structurally identical or not. Interestingly, it is one of the few problems that is not yet known to belong to either the P or NP-complete…
The symmetries of a finite graph are described by its automorphism group; in the setting of Woronowicz's quantum groups, a notion of a quantum automorphism group has been defined by Banica capturing the quantum symmetries of the graph. In…
It is unknown whether two graphs can be tested for isomorphism in polynomial time. A classical approach to the Graph Isomorphism Problem is the d-dimensional Weisfeiler-Lehman algorithm. The d-dimensional WL-algorithm can distinguish many…
A polynomial algorithm for graphs' isomorphism testing is constructed in assumption that there exists a corresponding polynomial algorithm for graphs with trivial automorphism group.
We relate the graph isomorphism problem to the solvability of certain systems of linear equations with nonnegative variables. This version replaces the two previous versions of this paper.
We introduce a new concept of a subgraph class called a superbubble for analyzing assembly graphs, and propose an efficient algorithm for detecting it. Most assembly algorithms utilize assembly graphs like the de Bruijn graph or the overlap…
Graph matching or quadratic assignment, is the problem of labeling the vertices of two graphs so that they are as similar as possible. A common method for approximately solving the NP-hard graph matching problem is relaxing it to a convex…
It is well-known [KST93] that the complexity of the Graph Automorphism problem is characterized by a special case of Graph Isomorphism, where the input graphs satisfy the "promise" of being rigid (that is, having no nontrivial…
This paper studies infinite graphs produced from a natural unfolding operation applied to finite graphs. Graphs produced via such operations are of finite degree and automatic over the unary alphabet (that is, they can be described by…
An automorphism of a graph is called quasi-semiregular if it fixes a unique vertex of the graph and its remaining cycles have the same length. This kind of symmetry of graphs was first investigated by Kutnar, Malni\v{c}, Mart\'{i}nez and…
The upcoming landscape of Earth Observation missions will defined by networked heterogeneous nanosatellite constellations required to meet strict mission requirements, such as revisit times and spatial resolution. However, scheduling…
The subgraph isomorphism finding problem is a well-studied problem in the field of computer science and graph theory, and it aims to enumerate all instances of a query graph in the respective data graph. In this paper, we propose an…
The graph identification problem consists of discovering the interactions among nodes in a network given their state/feature trajectories. This problem is challenging because the behavior of a node is coupled to all the other nodes by the…
Subgraph isomorphism counting is known as #P-complete and requires exponential time to find the accurate solution. Utilizing representation learning has been shown as a promising direction to represent substructures and approximate the…
Graph Isomorphism is one of the classical problems of graph theory for which no deterministic polynomial-time algorithm is currently known, but has been neither proven to be NP-complete. Several heuristic algorithms have been proposed to…