On the graph isomorphism problem (original) (raw)
Related papers
Graph isomorphism is polynomial
We relate the graph isomorphism problem to the solvability of certain systems of linear equations and linear inequalities. The number of these equations and inequalities is related to the complexity of the graphs isomorphism and subgraph isomorphim problems.
A Novel Algorithm for Isomorphic Graph
2013
The graph isomorphism difficulty is very famous; isomorphism problem is still one of the unsolved problems of graph theory. Here in this paper we are dealing with some applications of this problem and major idea behind this is advancement of some accessible graph isomorphism algorithms. In this paper we are also focusing on producing the solution for problems that seems like isomorphic problems but they are not exactly isomorphic
1993
Bibliographic information published by the Deutsche Nationalbibliothek The Deutsche Nationalbibliothek lists this publication in the Deutsche Nationalbibliografie; detailed bibliographic data are available in the Internet at http://dnb.d-nb.de. License This work is licensed under a Creative Commons Attribution 3.0 DE license (CC BY 3.0 DE). In brief, this license authorizes each and everybody to share (to copy, distribute and transmit) the work under the following conditions, without impairing or restricting the authors' moral rights: Attribution: The work must be attributed to its authors. The copyright is retained by the corresponding authors. Digital Object Identifier: 10.4230/DagRep.5.12.i Aims and Scope The periodical Dagstuhl Reports documents the program and the results of Dagstuhl Seminars and Dagstuhl Perspectives Workshops. In principal, for each Dagstuhl Seminar or Dagstuhl Perspectives Workshop a report is published that contains the following: an executive summary of the seminar program and the fundamental results, an overview of the talks given during the seminar (summarized as talk abstracts), and summaries from working groups (if applicable). This basic framework can be extended by suitable contributions that are related to the program of the seminar, e. g. summaries from panel discussions or open problem sessions.
The graph isomorphism problem on geometric graphs
Discrete Mathematics & Theoretical Computer Science, 2014
The graph isomorphism (GI) problem asks whether two given graphs are isomorphic or not. The GI problem is quite basic and simple, however, it's time complexity is a long standing open problem. The GI problem is clearly in NP, no polynomial time algorithm is known, and the GI problem is not NP-complete unless the polynomial hierarchy collapses. In this paper, we survey the computational complexity of the problem on some graph classes that have geometric characterizations. Sometimes the GI problem becomes polynomial time solvable when we add some restrictions on some graph classes. The properties of these graph classes on the boundary indicate us the essence of difficulty of the GI problem. We also show that the GI problem is as hard as the problem on general graphs even for grid unit intersection graphs on a torus, that partially solves an open problem.
A pr 2 01 6 Polynomial-time algorithm for determining the graph isomorphism
2016
To solve the problem of establishing isomorphism two connected undirected graphs, we use the methodology of positioning graph vertices relative to each other. Based on the position of the vertex in one of the graphs, it is determined the corresponding vertex in the other graph. For the selected vertex of the undirected graph, we define a neighborhood k-th (0 ≤ k ≤ n − 1) level, where n is the number of graph vertices. Next, we construct an auxiliary directed graph, generated by the selected vertex. The vertices of the digraph are positionable by special characteristics — vectors, which locate each vertex of the digraph relative the found neighborhoods. This enabled to develop an algorithm, the running time of which is equal to O(n4). MCS2000: 05C85, 68Q17.
Polynomial-time algorithm for determining the graph isomorphism (v.2)
2016
We develop the methodology of positioning graph vertices relative to each other to solve the problem of determining isomorphism of two undirected graphs. Based on the position of the vertex in one of the graphs, it is determined the corresponding vertex in the other graph. For the selected vertex of the undirected graph, we define the neighborhoods of the vertices. Next, we construct the auxiliary directed graph, spawned by the selected vertex. The vertices of the digraph are positioned by special characteristics --- vectors, which locate each vertex of the digraph relative the found neighborhoods. This enabled to develop the algorithm for determining graph isomorphism, the runing time of which is equal to O(n4)O(n^4)O(n4).
On the Parallel Parameterized Complexity of the Graph Isomorphism Problem
Lecture Notes in Computer Science, 2018
In this paper, we study the parallel and the space complexity of the graph isomorphism problem (GI) for several parameterizations. Let H = {H1, H2, • • • , H l } be a finite set of graphs where |V (Hi)| ≤ d for all i and for some constant d. Let G be an H-free graph class i.e., none of the graphs G ∈ G contain any H ∈ H as an induced subgraph. We show that GI parameterized by vertex deletion distance to G is in a parameterized version of AC 1 , denoted Para-AC 1 , provided the colored graph isomorphism problem for graphs in G is in AC 1. From this, we deduce that GI parameterized by the vertex deletion distance to cographs is in Para-AC 1. The parallel parameterized complexity of GI parameterized by the size of a feedback vertex set remains an open problem. Towards this direction we show that the graph isomorphism problem is in Para-TC 0 when parameterized by vertex cover or by twin-cover. Let G ′ be a graph class such that recognizing graphs from G ′ and the colored version of GI for G ′ is in logspace (L). We show that GI for bounded vertex deletion distance to G ′ is in L. From this, we obtain logspace algorithms for GI for graphs with bounded vertex deletion distance to interval graphs and graphs with bounded vertex deletion distance to cographs.
On Isomorphism of Graphs and the k-clique Problem
2005
In this paper we obtain two necessary-sufficient conditions for the isomorphism of graphs and propose two polynomial time algorithms based on them. We associate the so called bitableaux with the graphs, which are the usual adjacency and incidence matrices used in the matrix representation of graphs expressed in a bi-tabular form. We achieve, by application of suitable permutations (transpositions), the so called standard representation for these bitableaux to characterize the graphs uniquely. We also propose a polynomial time algorithm for the k-clique problem towards the end of the paper.
Reductions between the Subgraph Isomorphism Problem and Hamiltonian and SAT Problems
17th International Conference on Electronics, Communications and Computers (CONIELECOMP'07), 2007
Subgraph isomorphism (SI) detection is an important problem for several computer science subfields. In this paper we present a study of the Subgraph Isomorphism Problem (SIP) and its relation with the Hamiltonian cycles and SAT problems. In particular, we describe how instances of those problems can be solved throughout SI detection (using problems reductions). In our experiments we use an algorithm developed by the authors, which is capable to find all valid mappings in a SI instance. We performed several experiments, including cases for which there exists a known solution in polynomial time. In our analysis, we show the advantage and disadvantage of using a SI representation to solve Hamiltonian cycles and SAT problems.
Polynomial-time algorithm for determining the graph isomorphism
We develop the methodology of positioning graph vertices relative to each other to solve the problem of determining isomorphism of two undirected graphs. Based on the position of the vertex in one of the graphs, it is determined the corresponding vertex in the other graph. For the selected vertex of the undirected graph, we define the neighborhoods of the vertices. Next, we construct the auxiliary directed graph, spawned by the selected vertex. The vertices of the digraph are positioned by special characteristics --- vectors, which locate each vertex of the digraph relative the found neighborhoods. This enabled to develop the algorithm for determining graph isomorphism, the runing time of which is equal to O(n4)O(n^4)O(n4).