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Further results on graph equations for line graphs and n-th power graphs

Jin Akiyama, Hiroshi Era, Geoffrey Exoo
1981 Discrete Mathematics  
WC present solutions of seven graph equations i~v&ing the line graph, complement andn-th power operations. One such equation L(G) li = d gen~aalizes a result of lul. Aigner.  ...  In addition, some comments are made :about graphs satisfy@ G" = e.  ...  Acknowledgement The authors wish to thank; the referee for making many important comments. L  ... 
doi:10.1016/0012-365x(81)90001-7 fatcat:qha6g5ixsne2zhsysrxy3c2yna

The Nth Power Signed Graphs-Ii

P. Siva Kota Reddy, S. Vijay, V. Lokesha
2010 Zenodo  
In this paper, we present solutions of some signed graph switching equations involving the line signed graph, complement and nth power signed graph operations.  ...  We now characterize signed graphs whose line signed graphs and its n th power line signed graphs are switching equivalent. In the case of graphs the following result is due to J.  ...  [12] ) For any signed graph S = (G, σ), its n th power signed graph S n is balanced.  ... 
doi:10.5281/zenodo.814375 fatcat:affgxub6sbextlo2ryyas6hjz4

A network approach for power grid robustness against cascading failures [article]

Xiangrong Wang, Yakup Koç, Robert E. Kooij, Piet Van Mieghem
2015 arXiv   pre-print
This paper further investigates the impact of the topology on the Braess's paradox, and identifies specific sub-structures whose existence results in Braess's paradox.  ...  Specifically, the effective graph resistance is deployed as a metric for network expansions (by means of transmission line additions) of an existing power grid.  ...  ACKNOWLEDGMENT This research was supported by the China Scholarship Council (CSC) and by the NWO project RobuSmart, grant number 647.000.001.  ... 
arXiv:1505.06312v1 fatcat:oi4or4ywjjcyvk6itywzfepvzi

A network approach for power grid robustness against cascading failures

Xiangrong Wang, Yakup Koc, Robert E. Kooij, Piet Van Mieghem
2015 2015 7th International Workshop on Reliable Networks Design and Modeling (RNDM)  
This paper further investigates the impact of the topology on the Braess's paradox, and identifies specific sub-structures whose existence results in Braess's paradox in power grids.  ...  Specifically, the effective graph resistance is deployed as a metric for network expansions (by means of transmission line additions) of an existing power grid.  ...  ACKNOWLEDGMENT This research was supported by the China Scholarship Council (CSC) and by the NWO project RobuSmart, grant number 647.000.001.  ... 
doi:10.1109/rndm.2015.7325231 dblp:conf/mwcn/WangKKM15 fatcat:p5mddphepndexomtepqi6wq2te

Power Grid Decomposition Based on Vertex Cut Sets and Its Applications to Topology Control and Power Trading [article]

Shuai Wang, John Baillieul
2018 arXiv   pre-print
This paper extends our recent results on the iterative heuristics and proposes a fast grid decomposition algorithm based on vertex cut sets with the purpose of further reducing the computational cost.  ...  Accordingly, power grid optimization by means of short term line switching has been proposed and is typically formulated as a mixed integer programming problem by treating the state of the transmission  ...  the shift factor vector for read power at the k-th vertex cut set bus on lines in the i-th sub-graph.  ... 
arXiv:1803.05860v2 fatcat:hco43q7oy5dsbfenljmipi2eb4

Dual coupling networks

T H Davies
2006 Proceedings of the Institution of mechanical engineers. Part C, journal of mechanical engineering science  
Using dual graphs and dual couplings, it is shown how the dual of a coupling network can be found.  ...  Conversely, internal actions attributable to overconstraint cannot be seen and so are difficult to imagine. Such actions could result in fatigue failure.  ...  This result is now compared with the results of a virtual power equation using virtual motions and circuit actions for the action analysis of N þ in reference [1] .  ... 
doi:10.1243/09544062c09405 fatcat:vntorjk6rzah3ntopslcaam2s4

Realtime Index-Free Single Source SimRank Processing on Web-Scale Graphs [article]

Jieming Shi, Tianyuan Jin, Renchi Yang, Xiaokui Xiao, Yin Yang
2020 arXiv   pre-print
Further, SimPush provides rigorous result quality guarantees, and its high performance does not rely on any strong assumption of the underlying graph.  ...  Consequently, to our knowledge none of them is ideal for scenarios in which (i) query processing must be done in realtime, and (ii) the underlying graph G is massive, with frequent updates.  ...  PRSim is based on the main concepts of SLING, and further optimizes performance, especially for power-law graphs.  ... 
arXiv:2002.08082v1 fatcat:qp7ec3lclna5vgw3ye3kxup7l4

Power Grid Decomposition Based on Vertex Cut Sets and Its Applications to Topology Control and Power Trading

Shuai Wang, John Baillieul
2018 2018 IEEE Conference on Decision and Control (CDC)  
This paper extends our recent results on the iterative heuristics and proposes a fast grid decomposition algorithm based on vertex cut sets with the purpose of further reducing the computational cost.  ...  Accordingly, power grid optimization by means of short term line switching has been proposed and is typically formulated as a mixed integer programming problem by treating the state of the transmission  ...  the shift factor vector for read power at the k-th vertex cut set bus on lines in the i-th sub-graph.  ... 
doi:10.1109/cdc.2018.8619241 dblp:conf/cdc/WangB18a fatcat:gbsd3tzdtza5laazzfrjtvq4om

Realtime index-free single source SimRank processing on web-scale graphs

Jieming Shi, Tianyuan Jin, Renchi Yang, Xiaokui Xiao, Yin Yang
2020 Proceedings of the VLDB Endowment  
Further, SimPush provides rigorous result quality guarantees, and its high performance does not rely on any strong assumption of the graph.  ...  Consequently, to our knowledge none of them is ideal for scenarios in which (i) query processing must be done in realtime, and (ii) the underlying graph G is massive, with frequent updates.  ...  PRSim is based on the main concepts of SLING, and further optimizes performance, especially for power-law graphs.  ... 
doi:10.14778/3384345.3384347 fatcat:5u3inqcy3rdg3eicawix4dvxqa

Breaking of the site-bond percolation universality in networks

Filippo Radicchi, Claudio Castellano
2015 Nature Communications  
We discuss possible implications of our results in real networks, and provide additional insights on the anomalous nature of the percolation transition with null threshold.  ...  graphs with diverging second moment of the degree distribution.  ...  Acknowledgements We thank Marian Boguñá, Alessandro Flammini, and Romualdo Pastor-Satorras for a critical reading of the manuscript.  ... 
doi:10.1038/ncomms10196 pmid:26667155 pmcid:PMC4682156 fatcat:yvncp5os6vccbecxycshqntomq

One Breaker is Enough: Hidden Topology Attacks on Power Grids [article]

Deepjyoti Deka, Ross Baldick, Sriram Vishwanath
2015 arXiv   pre-print
We discuss necessary and sufficient conditions for feasible attacks using a novel graph-coloring based analysis and show that an optimal attack requires breaker status change at only ONE transmission line  ...  The adversary, however, is incapable of changing the value of any meter data and can only block recorded measurements on certain lines from being transmitted to the control center.  ...  Fig. 1 . 1 Generalized State Estimator for a power system form, ignoring measurement noise, we can write equations for received measurements as Fig. 2 .Fig. 3 . 23 Feasible graph coloring scheme on IEEE  ... 
arXiv:1506.04303v1 fatcat:l4q43tkifnhkna63wnihguc2fe

Multiple solutions approach to tackle circular flows in real power tracing

A.R. Abhyankar, S.A. Khaparde, S.A. Soman
2006 2006 IEEE Power Engineering Society General Meeting  
When the directed graph of power flow is cyclic, the graph theoretic approach is not able to proceed further, while the linear equations based approach may or may not fail depending on the distribution  ...  Two versions of real power tracing are popularly quoted: Linear equations based and Graph theoretic based. Both the methods make use of proportional sharing assumption.  ...  Further, every column has a single entry and hence the resulting matrix is extremely sparse. 2) Load Tracing: The power flow P lm on line lm can also be expressed as summation of load components, i.e.:  ... 
doi:10.1109/pes.2006.1708967 fatcat:nmlkrt2zorbwtfbh4grl5yzcga

Analysis of Dynamic Characteristics of Clutch-to-Clutch Shifting Control of an Automatic Transmission

Fu Yanxiao, Dong Peng, Cui Liangyi, Xu Xiangyang
2014 Sensors & Transducers  
results.  ...  For this very purpose, this paper introduces a simulation model of an 8-speed automatic transmission for front-drive vehicles with respect to detailed shifting strategies and relative parameters.  ...  Acknowledgements This project is supported by National Science and Technology Support Program "Key technology and industrialization of energy-saving and environmentfriend 8-speed automatic transmission  ... 
doaj:bede171978ad45f489865a17c9801b3c fatcat:xq2qv6ntgza7njq3jnwlyl25fq

A Graph Computation based Sequential Power Flow Calculation for Large-Scale ACDC Systems [article]

Wei Feng, Jingjin Wu, Chen Yuan, Guangyi Liu, Renchang Dai, Qingxin Shi, Fangxing Li
2019 arXiv   pre-print
This paper proposes a graph computation based sequential power flow calculation method for Line Commutated Converter (LCC) based large-scale AC/DC systems to achieve a high computing performance.  ...  Based on the graph theory, the complex AC/DC system is first converted to a graph model and stored in a graph database.  ...  Graph Database and Graph Modeling In graph database, a power system is modeled as a graph G (V, E), where ∈ represents the i th element of the vertex set V, and ∈ denotes the link between vertex i and  ... 
arXiv:1902.10192v1 fatcat:djzhosrz65h63ignlcs4ufqagu

Recurrent Graph Tensor Networks: A Low-Complexity Framework for Modelling High-Dimensional Multi-Way Sequence [article]

Yao Lei Xu, Danilo P. Mandic
2021 arXiv   pre-print
To this end, we develop a multi-linear graph filter framework for approximating the modelling of hidden states in RNNs, which is embedded in a tensor network architecture to improve modelling power and  ...  reduce parameter complexity, resulting in a novel Recurrent Graph Tensor Network (RGTN).  ...  Graph Signal Processing A graph G = {V, E} is defined by a set of N vertices (or nodes) v n ⊂ V for n = 1, . . . , N , and a set of edges connecting the n th and m th vertices e nm = (v n , v m ) ∈ E,  ... 
arXiv:2009.08727v5 fatcat:eoul7vqcrjd4zknyn3cfjbh3ki
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