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Page 7822 of Mathematical Reviews Vol. , Issue 2002K [page]

2002 Mathematical Reviews  
Summary: “We consider the zeta functions of the line graph and the middle graph of a regular covering of a graph G, and their related topics.  ...  For a regular graph G, we express the zeta functions of the line graph and the middle graph of a regular covering of G by using the characteristic polynomial of that regular covering.”  ... 

Zeta functions of line, middle, total graphs of a graph and their coverings

Jin Ho Kwak, Iwao Sato
2006 Linear Algebra and its Applications  
Furthermore, we discuss the L-functions of the line, middle and total graph of a regular graph G.  ...  We consider the (Ihara) zeta functions of line graphs, middle graphs and total graphs of a regular graph and their (regular or irregular) covering graphs.  ...  Mizuno and Sato [24] expressed the Bartholdi zeta functions of the line graph and the middle graph of a regular covering of a graph by using the characteristic polynomial of that regular covering.  ... 
doi:10.1016/j.laa.2006.01.033 fatcat:slg6zgruwnfffndlyvwvy2k3wy

Topology for Distributed Inference on Graphs

Soummya Kar, Saeed Aldosari, JosÉ M. F. Moura
2008 IEEE Transactions on Signal Processing  
We show that, under appropriate conditions, the topology given by the nonbipartite Ramanujan graphs optimizes the convergence rate of this distributed algorithm.  ...  Let decision-makers collaborate to reach a decision.  ...  In the panels of both Figures, the top line illustrates the re- For connected nonbipartite k-regular graphs, the eigenvalues (A), (A) are nontrivial.  ... 
doi:10.1109/tsp.2008.923536 fatcat:dgkw6yyovzabxfq4os6kno4uc4

Page 4876 of Mathematical Reviews Vol. , Issue 89I [page]

1989 Mathematical Reviews  
Ventre (Naples) 89i:05240 05C75 Topp, Jerzy (PL-TGDN) Graphs whose line graphs, middle graphs, and total graphs are comparability graphs.  ...  The author shows that the line graph L(G) of a graph G is a comparability graph if each connected  ... 

Page 6643 of Mathematical Reviews Vol. , Issue 92m [page]

1992 Mathematical Reviews  
The graph-valued functions studied in this paper are line graph, subdivision graph, independence graph, middle graph, point-line graph, total graph and semitotal (point) graph.” 92m:05195 05C99 Sierksma  ...  OSE Algebraic combinatorics 92m:05201 This result is a generalization of a theorem of Brualdi and Csima concerning matching extension in a regular bipartite graph.” 92m:05198 05D05 65310 Katepnuo Kana,  ... 

Spectral dynamics of guided edge removals and identifying transient amplifiers for death-Birth updating [article]

Hendrik Richter
2022 arXiv   pre-print
The algorithm starts with a regular input graph and iteratively removes edges until desired structures are achieved. Thus, a sequence of candidate graphs is obtained.  ...  Moreover, we are interested in the Laplacian spectra of the candidate graphs and analyze the iterative process by its spectral dynamics.  ...  Acknowledgments I wish to thank Markus Meringer for making available genreg [37] used for generating the regular input graphs and for helpful discussions, and Benjamin Allen for sharing the algorithm  ... 
arXiv:2204.12861v1 fatcat:sbt5k7dscbfx7d45b2lthf5eka

Topology for Distributed Inference on Graphs [article]

Soummya Kar, Saeed Aldosari, José M. F. Moura
2006 arXiv   pre-print
This reformulation avoids costly Monte Carlo simulations and leads to the class of non-bipartite Ramanujan graphs for which we find a lower bound on γ.  ...  We reformulate the topology design problem as a spectral graph design problem, namely, maximizing the eigenratio γ of two eigenvalues of the graph Laplacian L, a matrix that is naturally associated with  ...  This parameter is the ratio of the algebraic connectivity of the graph over the largest eigenvalue λ N (L) of the graph Laplacian L.  ... 
arXiv:cs/0606052v1 fatcat:r6wixtml5rgc7nztn675ppcxry

Construction of Reverse Super Edge Magic Total Graphs

U. Masthan Raju, S. Sharief Basha
2018 International Journal of Engineering & Technology  
In this paper, we investigate the adjacency matrix of reverse super edge magic vertex graph and use this graph to construct other reverse super edge magic graphs with the same edge weight set.  ...  Additionally, by combining known reverse super edge magic labelled graphs, we give a construction for a new reverse super edge magic graph  ...  • Can we use the algebraic properties of the adjacency matrix to find new properties of RSEM graph?  ... 
doi:10.14419/ijet.v7i4.10.20906 fatcat:jz7wb4tgdzbnbojloh2fvfyzzu

Effects of network topology on the performance of consensus and distributed learning of SVMs using ADMM

Shirin Tavara, Alexander Schliep
2021 PeerJ Computer Science  
We investigate the impact of network topology on the performance of an ADMM-based learning of Support Vector Machine using expander, and mean-degree graphs, and additionally some of the common modern network  ...  The Alternating Direction Method of Multipliers (ADMM) is a popular and promising distributed framework for solving large-scale machine learning problems.  ...  ACKNOWLEDGEMENTS The parallel computations in this article are performed on Hebbe at Chalmers Centre for Computational Science and Engineering (C3SE) provided by the Swedish National Infrastructure for  ... 
doi:10.7717/peerj-cs.397 pmid:33817043 pmcid:PMC7959654 fatcat:zgpyxponqjcefaylcbih2thz6m

Some physical and chemical indices of clique-inserted lattices

Zuhe Zhang
2013 Journal of Statistical Mechanics: Theory and Experiment  
The operation of replacing every vertex of an r-regular lattice H by a complete graph of order r is called clique-inserting, and the resulting lattice is called the clique-inserted-lattice of H.  ...  In this paper, we reveal the relationship between the energy and resistance distance of an r-regular lattice and that of its clique-inserted-lattice.  ...  It is well known that µ 2 , called the algebraic connectivity of G, is greater than 0 if and only if G is a connected graph.  ... 
doi:10.1088/1742-5468/2013/10/p10004 fatcat:hxugmuget5hancwt7dspglpiea

On the algebraic approach to cubic lattice Potts models

Srinandan Dasmahapatra, Paul Martin
1996 Journal of Physics A: Mathematical and General  
We consider Diagram algebras, (G) (generalized Temperley-Lieb algebras) defined for a large class of graphs G, including those of relevance for cubic lattice Potts models, and study their structure for  ...  We outline measures to extract the quotient algebra that would illuminate the physics of three dimensional Potts models.  ...  Trace the connectivities from bottom to top, and for each discarded part from the middle, pick up a factor of Q to obtain a • b.The Diagram algebra, D G (Q), for a graph G is defined as the subalgebra  ... 
doi:10.1088/0305-4470/29/2/006 fatcat:2svajtoezjarlbdpv5z7jfjlza

Supersymmetric correspondence in spectra on a graph and its line graph: From circuit theory to spoof plasmons on metallic lattices

Yosuke Nakata, Yoshiro Urade, Toshihiro Nakanishi, Fumiaki Miyamaru, Mitsuo Wada Takeda, Masao Kitano
2016 Physical Review A  
We investigate the supersymmetry (SUSY) structures for inductor-capacitor circuit networks on a simple regular graph and its line graph.  ...  Using terahertz time-domain spectroscopy, we demonstrate the band correspondence of fabricated metallic hexagonal and kagom\'e lattices.  ...  For m = 2, all spectra of the inductor-capacitor circuit networks on a simple connected m-regular graph G and its line graph L(G) coincide because of G = L(G).  ... 
doi:10.1103/physreva.93.043853 fatcat:kh2io66ppffrpeqydmj2uanglq

Examining How Teachers Use Graphs to Teach Mathematics during a Professional Development Program

Alfredo Bautista, M. C. Cañadas, Bárbara M. Brizuela, Analúcia D. Schliemann
2015 Journal of Education and Training Studies  
In this study, we analyzed how grades 5-9 mathematics teachers used graphs to teach mathematics at the start and end of a PD program.  ...  Results suggest that the features of the PD program had a positive effect on teachers' classroom practices regarding the use of graphs.  ...  The ideas expressed herein are those of the authors and do not necessarily reflect the ideas of the funding agency.  ... 
doi:10.11114/jets.v3i2.676 fatcat:xtbabfbtabbtbcqkh3hm2zklie

Pattern Generalization with Graphs and Words: A Cross-Sectional and Longitudinal Analysis of Middle School Students' Representational Fluency

Mitchell J. Nathan, Sunae Kim
2007 Mathematical Thinking and Learning  
Students do not necessarily make useful connections between discrete forms of representations such as a point-wise graph, and continuous forms such as a line graph of the same function.  ...  , or (b) a continuous (verbal rule or line graph) mode.  ... 
doi:10.1080/10986060701360886 fatcat:dvbtszry6jcrjdm3qiiholjsty

Representational disfluency in algebra: evidence from student gestures and speech

Kristen N. Bieda, Mitchell J. Nathan
2009 ZDM: Mathematics Education  
), while retaining the connection back to the linear pattern as graphed, were categorized as interpretatively grounded.  ...  Students who were classified as spatially grounded exhibited a bounded view of the graph that limited their ability to make far predictions until they physically altered the spatial configuration of the  ...  Acknowledgments This research was funded in part by a grant entitled ''Understanding and Cultivating the Transition from Arithmetic to Algebraic Reasoning,'' awarded to the second author by the Interagency  ... 
doi:10.1007/s11858-009-0198-0 fatcat:h2w6g7kcsnfknejp7a3tjlflca
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