Related papers: Graph Isomorphism and Circuit Size

In this note we prove that every closed graph $G$ is up to isomorphism a proper interval graph. As a consequence we obtain that there exist linear-time algorithms for closed graph recognition.

The Subgraph Isomorphism problem asks, given a host graph G on n vertices and a pattern graph P on k vertices, whether G contains a subgraph isomorphic to P. The restriction of this problem to planar graphs has often been considered. After…

In this paper we study the complexity of the following problems: Given a colored graph X=(V,E,c), compute a minimum cardinality set S of vertices such that no nontrivial automorphism of X fixes all vertices in S. A closely related problem…

The complexity of the graph isomorphism problem for trapezoid graphs has been open over a decade. This paper shows that the problem is GI-complete. More precisely, we show that the graph isomorphism problem is GI-complete for comparability…

We investigate the structure of conformally rigid graphs. Graphs are conformally rigid if introducing edge weights cannot increase (decrease) the second (last) eigenvalue of the Graph Laplacian. Edge-transitive graphs and distance-regular…

Modern methods of graph theory describe a graph up to isomorphism, which makes it difficult to create mathematical models for visualizing graph drawings on a plane. The topological drawing of the planar part of a graph allows representing…

The presented material is devoted to the equivalent conversion from the vertex graphs to the edge graphs. We suggest that the proved theorems solve the problem of the isomorphism of graphs, the problem of the graph's enumeration with the…

Let $G$ and $H$ be two simple graphs. A bijection $\phi:V(G)\rightarrow V(H)$ is called an isomorphism between $G$ and $H$ if $(\phi v_i)(\phi v_j)\in E(H)$ $\Leftrightarrow$ $v_i v_j\in E(G)$, $\forall v_i,v_j \in V(G)$. In the case that…

We describe a technique to determine the automorphism group of a geometrically represented graph, by understanding the structure of the induced action on all geometric representations. Using this, we characterize automorphism groups of…

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…

We describe a method for generating graphs that provide difficult examples for practical Graph Isomorphism testers. We first give the theoretical construction, showing that we can have a family of graphs without any non-trivial…

We investigate a special case of the Induced Subgraph Isomorphism problem, where both input graphs are interval graphs. We show the NP-hardness of this problem, and we prove fixed-parameter tractability of the problem with non-standard…

A commonly studied means of parameterizing graph problems is the deletion distance from triviality (Guo et al. 2004), which counts vertices that need to be deleted from a graph to place it in some class for which efficient algorithms are…

This article investigates the isomorphism problem for graphs derived from the four standard graph products: Cartesian, Kronecker (direct), strong, and lexicographic product. We provide a complete characterization of all simple connected…

In this paper, we study the graph classification problem from the graph homomorphism perspective. We consider the homomorphisms from $F$ to $G$, where $G$ is a graph of interest (e.g. molecules or social networks) and $F$ belongs to some…

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…

An isomorphism between two graphs is a bijection between their vertices that preserves the edges. We consider the problem of determining whether two finite undirected weighted graphs are isomorphic, and finding an isomorphism relating them…

This work is the extension of the results by the author in [7] and [6] for low-genus surfaces. Let $S$ be an orientable, connected surface of finite topological type, with genus $g \leq 2$, empty boundary, and complexity at least $2$; as a…

Subgraph isomorphism is a well-known NP-hard problem which is widely used in many applications, such as social network analysis and knowledge graph query. Its performance is often limited by the inherent hardness. Several insightful works…

In this paper, we propose algorithms for the graph isomorphism (GI) problem that are based on the eigendecompositions of the adjacency matrices. The eigenvalues of isomorphic graphs are identical. However, two graphs $ G_A $ and $ G_B $ can…