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A graph is said to be circular-arc if the vertices can be associated with arcs of a circle so that two vertices are adjacent if and only if the corresponding arcs overlap. It is proved that the isomorphism of circular-arc graphs can be…

Data Structures and Algorithms · Computer Science 2019-07-15 Roman Nedela , Ilia Ponomarenko , Peter Zeman

We use the concept of a Kirchhoff resistor network (alternatively random walk on a network) to probe connected graphs and produce symmetry revealing canonical labelings of the graph(s) nodes and edges.

Discrete Mathematics · Computer Science 2007-05-23 Matthew Delacorte

We give a linear-time algorithm that checks for isomorphism between two 0-1 matrices that obey the circular-ones property. This algorithm leads to linear-time isomorphism algorithms for related graph classes, including Helly circular-arc…

Data Structures and Algorithms · Computer Science 2013-09-18 Andrew R. Curtis , Min Chih Lin , Ross M. McConnell , Yahav Nussbaum , Francisco J. Soulignac , Jeremy P. Spinrad , Jayme L. Szwarcfiter

The graph isomorphism problem is considered. We assign modified $n$-variable characteristic polynomials for graphs and reduce the graph isomorphism problem to the problem of the polynomials isomorphism. It is required to find out, is there…

Discrete Mathematics · Computer Science 2024-10-18 Alexander Prolubnikov

In this paper, we show that given a weighted, directed planar graph $G$, and any $\epsilon >0$, there exists a polynomial time and $O(n^{\frac{1}{2}+\epsilon})$ space algorithm that computes the shortest path between two fixed vertices in…

Computational Complexity · Computer Science 2015-02-10 Diptarka Chakraborty , Raghunath Tewari

This article deals with new polynomial time algorithm for graph isomorphism testing.

Data Structures and Algorithms · Computer Science 2013-06-19 Michael I. Trofimov

IC-planar graphs are those graphs that admit a drawing where no two crossed edges share an end-vertex and each edge is crossed at most once. They are a proper subfamily of the 1-planar graphs. Given an embedded IC-planar graph $G$ with $n$…

Computational Geometry · Computer Science 2016-07-19 Franz J. Brandenburg , Walter Didimo , William S. Evans , Philipp Kindermann , Giuseppe Liotta , Fabrizio Montecchiani

We consider the following two algorithmic problems: given a graph $G$ and a subgraph $H\subseteq G$, decide whether $H$ is an isometric or a geodesically convex subgraph of $G$. It is relatively easy to see that the problems can be solved…

Data Structures and Algorithms · Computer Science 2026-04-14 Sergio Cabello

The monography examines the problem of constructing a group of automorphisms of a graph. A graph automorphism is a mapping of a set of vertices onto itself that preserves adjacency. The set of such automorphisms forms a vertex group of a…

History and Overview · Mathematics 2024-07-18 Sergey Kurapov , Maxim Davidovsky

We present the first parallel fixed-parameter algorithm for subgraph isomorphism in planar graphs, bounded-genus graphs, and, more generally, all minor-closed graphs of locally bounded treewidth. Our randomized low depth algorithm has a…

Data Structures and Algorithms · Computer Science 2020-07-03 Lukas Gianinazzi , Torsten Hoefler

It is well known that the graph isomorphism problem is polynomial-time reducible to the graph automorphism problem (in fact these two problems are polynomial-time equivalent). We show that, analogously, the group isomorphism problem is…

Computational Complexity · Computer Science 2025-03-04 Saveliy V. Skresanov

We investigate classical and quantum physics-based algorithms for solving the graph isomorphism problem. Our work integrates and extends previous work by Gudkov et al. (cond-mat/0209112) and by Rudolph (quant-ph/0206068). Gudkov et al.…

Quantum Physics · Physics 2007-05-23 Shiue-yuan Shiau , Robert Joynt , S. N. Coppersmith

Motivated by the problem of matching vertices in two correlated Erd\H{o}s-R\'enyi graphs, we study the problem of matching two correlated Gaussian Wigner matrices. We propose an iterative matching algorithm, which succeeds in polynomial…

Data Structures and Algorithms · Computer Science 2025-09-01 Jian Ding , Zhangsong Li

We consider complete graphs with edge weights and/or node weights taking values in some set. In the first part of this paper, we show that a large number of graphs are completely determined, up to isomorphism, by the distribution of their…

Combinatorics · Mathematics 2007-10-11 Mireille Boutin , Gregor Kemper

Graphs are widely used to model complicated data semantics in many application domains. In this paper, two novel and efficient algorithms Fast-ON and Fast-P are proposed for solving the subgraph isomorphism problem. The two algorithms are…

Data Structures and Algorithms · Computer Science 2019-04-19 Mosab Hassaan , Karam Gouda

In some applications of matching, the structural or hierarchical properties of the two graphs being aligned must be maintained. The hierarchical properties are induced by the direction of the edges in the two directed graphs. These…

Data Structures and Algorithms · Computer Science 2009-09-29 Sean M. Falconer , Dmitri Maslov

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…

Computational Complexity · Computer Science 2007-05-23 Marats Golovkins

The graph isomorphism problem is theoretically interesting and also has many practical applications. The best known classical algorithms for graph isomorphism all run in time super-polynomial in the size of the graph in the worst case. An…

Quantum Physics · Physics 2011-04-26 David Rosenbaum

This paper considers the problem of distributed optimization over time-varying graphs. For the case of undirected graphs, we introduce a distributed algorithm, referred to as DIGing, based on a combination of a distributed inexact gradient…

Optimization and Control · Mathematics 2017-03-21 Angelia Nedich , Alex Olshevsky , Wei Shi

Given a graph $G$, the graph $[G]$ obtained by adding, for each pair of vertices of $G$, a unique vertex adjacent to both vertices is called the binding graph of $G$. In this work, we show that the class of binding graphs is…

Combinatorics · Mathematics 2024-08-27 Rui Xue