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On several symmetry conditions for graphs

Xingxing Yu
1992 Discrete Mathematics  
., On several symmetry conditions for graphs, Discrete Mathematics 102 (1992) 51-59. In this paper we deal with simple graphs.  ...  We investigate vertex-transitivity, edge-transitivity and symmetry of graphs, especially the relationships among them. We first give an equivalent condition for a graph to be vertex-transitive.  ...  Hemminger for their help. Also he would like to thank Prof. B. Alspach and the Referee for their suggestions.  ... 
doi:10.1016/0012-365x(92)90346-h fatcat:vjebffbm3zhnta65eqmin5yqqq

Perception of Symmetries in Drawings of Graphs [article]

Felice De Luca, Stephen Kobourov, Helen Purchase
2018 arXiv   pre-print
Symmetry is an important factor in human perception in general, as well as in the visualization of graphs in particular.  ...  We report the results of a human subjects experiment to determine what types of symmetries are more salient in drawings of graphs.  ...  Acknowledgements We thank Eric Welch for help with the experiment, Hang Chen for help with statistics, and yFiles for providing their software for research and education.  ... 
arXiv:1808.01031v3 fatcat:3tt3rtdm6fh6nnhcpiie3ice34

Fast computation of symmetries in boolean functions

A. Mishchenko
2003 IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems  
Symmetry detection in completely specified Boolean functions is important for several applications in logic synthesis, technology mapping, BDD minimization, and testing.  ...  The computation is particularly efficient when the functions have multiple symmetries or no symmetries.  ...  Thus, if two variables have several symmetries, the corresponding vertices are connected by as many edges of different type. Several graph operations are used in the sequel.  ... 
doi:10.1109/tcad.2003.818371 fatcat:nhnqurdu4ffn7pqqgrsxqdgcdi

Techniques for Distributed Reachability Analysis with Partial Order and Symmetry based Reductions [article]

Janardan Misra, Suman Roy
2009 arXiv   pre-print
We consider variants for both depth-first as well as breadth-first based generation of the reduced state graphs on-the-fly.  ...  In this work we propose techniques for efficient reachability analysis of the state space (e.g., detection of bad states) using a combination of partial order and symmetry based reductions in a distributed  ...  Several subtasks can be performed in parallel on different processors.  ... 
arXiv:0901.0179v1 fatcat:7anazzroereh7jdxrrteki5vaq

Graph Theory

Jose Rodriguez
2018 Symmetry  
This book contains the successful invited submissions [1-10] to a special issue of Symmetry on the subject area of 'graph theory'.  ...  This special issue includes the novel techniques and tools for graph theory, such as:  ...  • Local metric dimension of graphs [1] . • Gromov hyperbolicity on geometric graphs [2, 3, 5 ]. • Beta-differential of graphs [4] . • Path ordinal method [6] . • Neural networks on multi-centrality-index  ... 
doi:10.3390/sym10010032 fatcat:gglu7jodz5ck3cezrhurg6kcia

Fast Graph Fourier Transforms Based on Graph Symmetry and Bipartition

Keng-Shih Lu, Antonio Ortega
2019 IEEE Transactions on Signal Processing  
Though butterfly stages based on graph topological symmetry cannot be used for general graphs, they are useful in applications, including video compression and human action analysis, where symmetric graphs  ...  We also propose a graph decomposition method based on graph topological symmetry, which allows us to identify and exploit butterfly structures in stages.  ...  This necessary condition for φ-symmetry allows us to prune the involution search.  ... 
doi:10.1109/tsp.2019.2932882 fatcat:74xcyzu2bzcr7efm24nkseze2m

Querying subgraph sets with g-tries

Pedro Ribeiro, Fernando Silva
2012 Proceedings of the 2nd ACM SIGMOD Workshop on Databases and Social Networks - DBSocial '12  
In this paper we present an universal methodology for finding all the occurrences of a given set of subgraphs in one single larger graph.  ...  Using a specialized canonical form and symmetry breaking conditions, a single non-redundant search of the entire set of subgraphs is possible.  ...  Figure 3 : 3 Symmetry breaking conditions example. Figure 4 : 4 A g-trie with symmetry breaking conditions.  ... 
doi:10.1145/2304536.2304541 dblp:conf/dbsocial/RibeiroS12 fatcat:hcfuluqavvg3noxtwfmcp2krde

Faster symmetry discovery using sparsity of symmetries

Paul T. Darga, Karem A. Sakallah, Igor L. Markov
2008 Proceedings of the 45th annual conference on Design automation - DAC '08  
By avoiding quadratic runtime on large graphs, it improves state-ofthe-art runtimes from several days to less than a second.  ...  However, existing tools suffer quadratic runtime in the number of symmetries explicitly returned and are of limited use on very large, sparse, symmetric graphs.  ...  Junttila and Kaski [9] made several additional improvements in sparse graph symmetry discovery with their program bliss.  ... 
doi:10.1145/1391469.1391509 dblp:conf/dac/DargaSM08 fatcat:mdmdhej7bvdyxi3mmew47k2b5i

Consensus Graphs for Symmetry Plane Estimation [chapter]

Andrea Albarelli, Marcello Pelillo, Sebastiano Viviani
2008 Lecture Notes in Computer Science  
Finding the most relevant symmetry planes for an object is a key step in many computer vision and object recognition tasks.  ...  In this paper we introduce a new weighted association graph which relates the main symmetry planes of 3D objects to large sets of tightly coupled vertices.  ...  We thank Luxottica Group S.p.A. for funding this research and providing the experimental data.  ... 
doi:10.1007/978-3-540-89689-0_24 fatcat:jsp5m3bgmvdurcktx2ndnhfovm

Multiple Minimum Support-Based Rare Graph Pattern Mining Considering Symmetry Feature-Based Growth Technique and the Differing Importance of Graph Elements

Gangin Lee, Unil Yun, Heungmo Ryang, Donggyu Kim
2015 Symmetry  
(2) multiple minimum support thresholds suitable for each graph element.  ...  However, traditional ones do not consider such features.  ...  several additional considerations.  ... 
doi:10.3390/sym7031151 fatcat:gtzjlp7zkjcq3gok2ksaguteui

NemoMap: Improved Motif-centric Network Motif Discovery Algorithm

Tien Huynh, Somadina Mbadiwe, Wooyoung Kim
2018 Advances in Science, Technology and Engineering Systems  
Currently, there are two categories for network motif detection method: network-centric and motif-centric approach.  ...  Network motif analysis has several applications in many different fields such as biological study and social network modeling, yet motif detection tools are still limited by the intensive computation.  ...  Acknowledgment We thank the Computing and Software Systems, School of STEM, at the University of Washington Bothell for the support of this research.  ... 
doi:10.25046/aj030523 fatcat:wsl2iawvkvdmnk3xlv45ugylxa

Argumentation and graph properties

Mamadou Bilo Doumbouya, Bernard Kamsu-Foguem, Hugues Kenfack
2016 Information Processing & Management  
In this work, we combine several graph properties to provide three main propositions; one for identifying accepted arguments under the admissible, preferred semantics and the other to easily identify stable  ...  The principle of this method is to combine mathematical properties (e.g. symmetry, asymmetry, strong connectivity and irreflexivity) of graphs built from the argumentation system to compute sets of accepted  ...  Several of these studies are focused on one graph property i.e. symmetry for Coste-Marquis et al. (2005) even if they combine the property of symmetry and irreflexivity and strong connectivity for Baroni  ... 
doi:10.1016/j.ipm.2015.08.003 fatcat:27r4sriko5arpoq2ggdg223bgq

Classical symmetries and the Quantum Approximate Optimization Algorithm [article]

Ruslan Shaydulin, Stuart Hadfield, Tad Hogg, Ilya Safro
2021 arXiv   pre-print
The connection is general and includes but is not limited to problems defined on graphs.  ...  We provide numerical evidence that a small set of graph symmetry properties suffices to predict the minimum QAOA depth required to achieve a target approximation ratio on the MaxCut problem, in a practically  ...  R.S. is grateful to KBR, the QuAIL group, and the NASA Ames Research Center for the internship opportunity that enabled this research. R.S. and I.  ... 
arXiv:2012.04713v2 fatcat:sdu4nx5ogfaxzcf35kkpeme2jy

Global Symmetries, Local Symmetries and Groupoids

Michel Petitjean
2021 Symmetry  
Examples are given for graphs and networks, color symmetry and tilings. The definition of local symmetry in physics is also discussed.  ...  Local symmetries are primarily defined in the case of spacetime, but several authors have defined them outside this context, sometimes with the help of groupoids.  ...  It is a sufficient condition to have the symmetry group of φ G reduced to one element (the identity), and φ G is not symmetric for δ G .  ... 
doi:10.3390/sym13101905 fatcat:dpvyfw6qyfctvjwshnyzprma54

Sinkhorn algorithm for quantum permutation groups [article]

Ion Nechita, Simon Schmidt, Moritz Weber
2019 arXiv   pre-print
We introduce a Sinkhorn-type algorithm for producing quantum permutation matrices encoding symmetries of graphs.  ...  We apply it to the question whether a given finite graph (without multiple edges) has quantum symmetries in the sense of Banica.  ...  The authors would like to thank Piotr So ltan and Laura Mančinska for very useful discussions around some of the topics of this work.  ... 
arXiv:1911.04912v1 fatcat:dzjb2ywj4beedep7s6jz7pb7im
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