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A combinatorial interpretation of double base number system and some consequences
1.  Center for Information Security and Cryptography, University of Calgary, 2500 University Drive NW, Calgary, AB T2N 1N4, Canada, Canada 
[1] 
David Auger, Irène Charon, Iiro Honkala, Olivier Hudry, Antoine Lobstein. Edge number, minimum degree, maximum independent set, radius and diameter in twinfree graphs. Advances in Mathematics of Communications, 2009, 3 (1) : 97114. doi: 10.3934/amc.2009.3.97 
[2] 
Litao Guo, Bernard L. S. Lin. Vulnerability of super connected split graphs and bisplit graphs. Discrete & Continuous Dynamical Systems  S, 2019, 12 (4&5) : 11791185. doi: 10.3934/dcdss.2019081 
[3] 
Srimathy Srinivasan, Andrew Thangaraj. Codes on planar Tanner graphs. Advances in Mathematics of Communications, 2012, 6 (2) : 131163. doi: 10.3934/amc.2012.6.131 
[4] 
Cristina M. Ballantine. Ramanujan type graphs and bigraphs. Conference Publications, 2003, 2003 (Special) : 7882. doi: 10.3934/proc.2003.2003.78 
[5] 
Daniele D'angeli, Alfredo Donno, Michel Matter, Tatiana Nagnibeda. Schreier graphs of the Basilica group. Journal of Modern Dynamics, 2010, 4 (1) : 167205. doi: 10.3934/jmd.2010.4.167 
[6] 
Yong Lin, Gábor Lippner, Dan Mangoubi, ShingTung Yau. Nodal geometry of graphs on surfaces. Discrete & Continuous Dynamical Systems  A, 2010, 28 (3) : 12911298. doi: 10.3934/dcds.2010.28.1291 
[7] 
Dina Ghinelli, Jennifer D. Key. Codes from incidence matrices and line graphs of Paley graphs. Advances in Mathematics of Communications, 2011, 5 (1) : 93108. doi: 10.3934/amc.2011.5.93 
[8] 
Renato Iturriaga, Héctor Sánchez Morgado. The LaxOleinik semigroup on graphs. Networks & Heterogeneous Media, 2017, 12 (4) : 643662. doi: 10.3934/nhm.2017026 
[9] 
Thomas Zaslavsky. Quasigroup associativity and biased expansion graphs. Electronic Research Announcements, 2006, 12: 1318. 
[10] 
Braxton Osting, Jérôme Darbon, Stanley Osher. Statistical ranking using the $l^{1}$norm on graphs. Inverse Problems & Imaging, 2013, 7 (3) : 907926. doi: 10.3934/ipi.2013.7.907 
[11] 
Fabio Camilli, Adriano Festa, Silvia Tozza. A discrete Hughes model for pedestrian flow on graphs. Networks & Heterogeneous Media, 2017, 12 (1) : 93112. doi: 10.3934/nhm.2017004 
[12] 
Luca Schenato, Sandro Zampieri. On rendezvous control with randomly switching communication graphs. Networks & Heterogeneous Media, 2007, 2 (4) : 627646. doi: 10.3934/nhm.2007.2.627 
[13] 
Joachim von Below, José A. Lubary. Isospectral infinite graphs and networks and infinite eigenvalue multiplicities. Networks & Heterogeneous Media, 2009, 4 (3) : 453468. doi: 10.3934/nhm.2009.4.453 
[14] 
Jeremias Epperlein, Stefan Siegmund. Phaselocked trajectories for dynamical systems on graphs. Discrete & Continuous Dynamical Systems  B, 2013, 18 (7) : 18271844. doi: 10.3934/dcdsb.2013.18.1827 
[15] 
Bruno Colbois, Alexandre Girouard. The spectral gap of graphs and Steklov eigenvalues on surfaces. Electronic Research Announcements, 2014, 21: 1927. doi: 10.3934/era.2014.21.19 
[16] 
ShuiNee Chow, Wuchen Li, Haomin Zhou. Entropy dissipation of FokkerPlanck equations on graphs. Discrete & Continuous Dynamical Systems  A, 2018, 38 (10) : 49294950. doi: 10.3934/dcds.2018215 
[17] 
Enrico Capobianco. Born to be big: Data, graphs, and their entangled complexity. Big Data & Information Analytics, 2016, 1 (2&3) : 163169. doi: 10.3934/bdia.2016002 
[18] 
Rinaldo M. Colombo, Mauro Garavello. Stability and optimization in structured population models on graphs. Mathematical Biosciences & Engineering, 2015, 12 (2) : 311335. doi: 10.3934/mbe.2015.12.311 
[19] 
Robert Carlson. Dirichlet to Neumann maps for infinite quantum graphs. Networks & Heterogeneous Media, 2012, 7 (3) : 483501. doi: 10.3934/nhm.2012.7.483 
[20] 
M. DeDeo, M. Martínez, A. Medrano, M. Minei, H. Stark, A. Terras. Spectra of Heisenberg graphs over finite rings. Conference Publications, 2003, 2003 (Special) : 213222. doi: 10.3934/proc.2003.2003.213 
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