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Canonical labeling of graphs

László Babai, Eugene M. Luks
1983 Proceedings of the fifteenth annual ACM symposium on Theory of computing - STOC '83  
Babai, On the complexity of canonical labeling of strongly regular graphs, SIA}i J. Comp. 9 (1980), 212-216. L. Babai, Moderately exponential bound for graph isomorphism,  ...  We compute canonical forms and the associated canonical labelings (or renumberings) in polynomial time for graphs of bounded v@$@nce, in moderately exponential, exp(n ~ + °tIJ),time for general graphs,  ...  Canonical forms 2.1 Canonical labeling-cosets.  ... 
doi:10.1145/800061.808746 dblp:conf/stoc/BabaiL83 fatcat:4selecxs5jgglevz3e7ldy7gni

Canonical Labelling of Site Graphs

Nicolas Oury, Michael Pedersen, Rasmus Petersen
2013 Electronic Proceedings in Theoretical Computer Science  
We first show that the problem of canonical labelling of site graphs reduces to the problem of canonical labelling of graphs with edge colourings.  ...  We investigate algorithms for canonical labelling of site graphs, i.e. graphs in which edges bind vertices on sites with locally unique names.  ...  The work of the second author was supported by an EPSRC Postdoctoral Fellowship (EP/H027955/1).  ... 
doi:10.4204/eptcs.116.3 fatcat:2eflqhd6njgxdjaxrv644yusdu

Search Space Contraction in Canonical Labeling of Graphs [article]

Adolfo Piperno
2011 arXiv   pre-print
The individualization-refinement paradigm for computing a canonical labeling and the automorphism group of a graph is investigated.  ...  It is shown that the approach presented here leads to a huge reduction in the search space, thereby making computation feasible for several classes of graphs which are hard for all the main canonical labeling  ...  Acknowledgments I would like to thank my friends and colleagues Maurizio Bonuccelli, Angelo Monti and Riccardo Silvestri for their suggestions and discussions about the topics of this paper.  ... 
arXiv:0804.4881v2 fatcat:wuyn4nnhbfeh3nbstcypecouem

Antimagic labeling and canonical decomposition of graphs

Michael D. Barrus
2010 Information Processing Letters  
RESEARCH INTERESTS AND EXPERIENCE Graph theory and combinatorics, with emphasis in structural and extremal graph theory. Refereed Journal Publications [1] (with Stephen G.  ...  Hartke and Mohit Kumbhat) Graph classes characterized both by forbidden subgraphs and degree sequences.  ...  [2] Antimagic labeling and canonical decomposition of graphs. Information Processing Letters, vol. 110 (2010), pp. 261-263. [3] (with Douglas B.  ... 
doi:10.1016/j.ipl.2010.01.006 fatcat:rdww2pkvuza4lbbzjwotqstamm

Analysis of a Canonical Labeling Algorithm for the Alignment of Correlated Erdős-Rényi Graphs [article]

Osman Emre Dai, Daniel Cullina, Negar Kiyavash, Matthias Grossglauser
2019 arXiv   pre-print
In this work we identify a region in which a straightforward O(n^11/5log n )-time canonical labeling algorithm, initially introduced in the context of graph isomorphism, succeeds in aligning correlated  ...  Graph alignment in two correlated random graphs refers to the task of identifying the correspondence between vertex sets of the graphs.  ...  If the canonical labeling scheme is robust in the sense that small differences in the structure of the graph induce small perturbations on the labels of vertices, then the canonical labeling can still  ... 
arXiv:1804.09758v2 fatcat:spsmi4snfzakhlyrxmh5qc24gy

Apply Partition Tree to Compute Canonical Labelings of Graphs

HAO Jian-Qiang, GONG Yun-Zhan, Tan Li, Duan Da-Gao
2016 International Journal of Grid and Distributed Computing  
while calculating the canonical labeling.  ...  To fix the glitch of Nauty, Traces [20] uses the strategy of breadth-first search to find the automorphism group and the canonical labeling.  ...  The Canonical Labeling of a graph G The first row of the upper triangular part of A(G) is the canonical labeling piece 1 of C(G), denoted by C 1 (G).  ... 
doi:10.14257/ijgdc.2016.9.5.21 fatcat:gdxoz75qgncjjk4h64jfcreqom

Use the K-Neighborhood Subgraphs to Compute Canonical Labelings of Graphs

Hao, Gong, Sun, Tan
2019 Mathematics  
It shows the correlation between the canonical labeling of a graph and the canonical labeling of its complement graph.  ...  It regularly examines the link between computing the canonical labeling of a graph and the canonical labeling of its o p e n k-n e i g h b o r h o o d s u b g r a p h.  ...  Conflicts of Interest: The authors declare no conflict of interest.  ... 
doi:10.3390/math7080690 fatcat:qzg4fen6afaadpxpa3gkde4upm

A Practical Graph Isomorphism Algorithm with Vertex Canonical Labeling

Aimin Hou, Qingqi Zhong, Yurou Chen, Zhifeng Hao
2014 Journal of Computers  
The vertex canonical labeling technique is one of the powerful methods in solving the graph isomorphism problem.  ...  In this paper, we advance a new method of vertex canonical labeling and propose a complete graph isomorphism algorithm with depth-first backtracking.  ...  ACKNOWLEDGMENT This work was supported by the National Natural Science Foundation of China (F020107) and the Natural Science Foundation of Guangdong Province, P.R.C. (9251009001000005).  ... 
doi:10.4304/jcp.9.10.2467-2474 fatcat:44rg7z4fgbcfdhxd76rpjkbnu4

Canonical Decomposition, Realizer, Schnyder Labeling and Orderly Spanning Trees of Plane Graphs [chapter]

Kazuyuki Miura, Machiko Azuma, Takao Nishizeki
2004 Lecture Notes in Computer Science  
A canonical decomposition, a realizer, a Schnyder labeling and an orderly spanning tree of a plane graph play an important role in straight-line grid drawings, convex grid drawings, floor-plannings, graph  ...  In this paper, we present a necessary and sufficient condition for their existence, and show that a canonical decomposition, a realizer, a Schnyder labeling, an orderly spanning tree, and an outer triangular  ...  A canonical decomposition, a realizer, a Schnyder labeling and an orderly spanning tree of a plane graph G play an important role in straight-line drawings, convex grid drawings, floor-plannings, graph  ... 
doi:10.1007/978-3-540-27798-9_34 fatcat:rc6ux56hdzh2rfkivijeyhakqq

CANONICAL DECOMPOSITION, REALIZER, SCHNYDER LABELING AND ORDERLY SPANNING TREES OF PLANE GRAPHS

KAZUYUKI MIURA, MACHIKO AZUMA, TAKAO NISHIZEKI
2005 International Journal of Foundations of Computer Science  
A canonical decomposition, a realizer, a Schnyder labeling and an orderly spanning tree of a plane graph play an important role in straight-line grid drawings, convex grid drawings, floor-plannings, graph  ...  In this paper, we present a necessary and sufficient condition for their existence, and show that a canonical decomposition, a realizer, a Schnyder labeling, an orderly spanning tree, and an outer triangular  ...  A canonical decomposition, a realizer, a Schnyder labeling and an orderly spanning tree of a plane graph G play an important role in straight-line drawings, convex grid drawings, floor-plannings, graph  ... 
doi:10.1142/s0129054105002905 fatcat:xnxog6szmfcsjox3nkxpeqlbya

Engineering an Efficient Canonical Labeling Tool for Large and Sparse Graphs [chapter]

Tommi Junttila, Petteri Kaski
2007 2007 Proceedings of the Ninth Workshop on Algorithm Engineering and Experiments (ALENEX)  
The problem of canonically labeling a graph is studied.  ...  graphs are developed.  ...  The authors thank Jani Jaakkola and Pekka Niklander at the Department of Computer Science of University of Helsinki for providing computing resources for the experiments.  ... 
doi:10.1137/1.9781611972870.13 dblp:conf/alenex/JunttilaK07 fatcat:c5tcgchf5jfjbg5ww5l65k6gvu

Fast Canonical Labelling for Graph based Data Mining

D. Kavitha, V. Kamakshi Prasad, J. V. R. Murthy
2017 International Journal of Advanced Research in Computer Science and Software Engineering  
of symmetric nodes in the canonical labelling process.The proposed technique reduces computation time by reversing the traditional labelling process which starts from the leaves and by eliminating the  ...  In this work, we present an algorithm to discover isomorphic graphs using canonical labelling that overcomes this problem based on the symmetries present in the graph, which eliminates the permutation  ...  Canonical labelling of a graph consists of assigning a unique label to a graph such that the label is invariant under isomorphism.  ... 
doi:10.23956/ijarcsse/sv7i5/0145 fatcat:w3d4l2ft4jg4hkm2yarhvxtv5u

Analysis of a Canonical Labeling Algorithm for the Alignment of Correlated Erdos-Rényi Graphs

Osman Emre Dai, Daniel Cullina, Negar Kiyavash, Matthias Grossglauser
2019 Proceedings of the ACM on Measurement and Analysis of Computing Systems  
In this work we identify a region in which a straightforward O(n 11/5 log n)-time canonical labeling algorithm, initially introduced in the context of graph isomorphism, succeeds in aligning correlated  ...  Graph alignment in two correlated random graphs refers to the task of identifying the correspondence between vertex sets of the graphs.  ...  If the canonical labeling scheme is robust in the sense that small differences in the structure of the graph induce small perturbations on the labels of vertices, then the canonical labeling can still  ... 
doi:10.1145/3341617.3326151 fatcat:lw4vjkn6vrgmjoewcyqbg6mvgm

Comment on "Isomorphism, Automorphism Partitioning, and Canonical Labeling Can Be Solved in Polynomial-Time for Molecular Graphs"

Bo Tao Fan, Annick Panaye, Jean-Pierre Doucet
1999 Journal of chemical information and computer sciences  
The nodes 2 and 4 of the example graph are constitutionally equivalent.  ...  In this figure, for Faulon's graph, the vectors of numbers of nonrepetitive nodes are (3,5,5,2) for MINST(1), and (3,6,5,1) for MINST(8), respectively.  ... 
doi:10.1021/ci980155e fatcat:lb2g6c6n2fb7bojxqyarlvvj5i

Reconfigurable Hardware Acceleration of Canonical Graph Labelling [chapter]

David B. Thomas, Wayne Luk, Michael Stumpf
Lecture Notes in Computer Science  
This paper proposes an architecture to allow acceleration of sub-graph identification through reconfigurable hardware, using a canonical graph labelling algorithm.  ...  A practical implementation of the canonical labelling algorithm in the Virtex-4 reconfigurable architecture is presented, examining the scaling of resource usage and speed with changing algorithm parameters  ...  Canonical Labelling Algorithm Canonical labelling is the process of attaching a unique label to graphs, such that any two graphs with the same structure will receive the same label, and any two graphs  ... 
doi:10.1007/978-3-540-71431-6_28 dblp:conf/arc/ThomasLS07 fatcat:s3yrngaobrhrbdyl3dn27fag3e
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