Zhan, Hanmeng Factoring discrete-time quantum walks on distance regular graphs into continuous-time quantum walks. (English) Zbl 1496.81061 Linear Algebra Appl. 648, 88-103 (2022). MSC: 81Q35 05C81 05C50 60K50 60J35 82B41 PDFBibTeX XMLCite \textit{H. Zhan}, Linear Algebra Appl. 648, 88--103 (2022; Zbl 1496.81061) Full Text: DOI arXiv
Ghorbani, Ebrahim; Koohestani, Masoumeh Spectral classes of strongly-regular and distance-regular graphs. (English) Zbl 1493.05294 Linear Algebra Appl. 641, 182-199 (2022). Reviewer: Andrea Svob (Rijeka) MSC: 05E30 05C50 05C75 PDFBibTeX XMLCite \textit{E. Ghorbani} and \textit{M. Koohestani}, Linear Algebra Appl. 641, 182--199 (2022; Zbl 1493.05294) Full Text: DOI
Howlader, Aditi; Panigrahi, Pratima On the distance spectrum of minimal cages and associated distance biregular graphs. (English) Zbl 1480.05044 Linear Algebra Appl. 636, 115-133 (2022). MSC: 05C12 05C50 PDFBibTeX XMLCite \textit{A. Howlader} and \textit{P. Panigrahi}, Linear Algebra Appl. 636, 115--133 (2022; Zbl 1480.05044) Full Text: DOI arXiv
Martin, William J. Scaffolds: a graph-theoretic tool for tensor computations related to Bose-Mesner algebras. (English) Zbl 1462.05362 Linear Algebra Appl. 619, 50-106 (2021). MSC: 05E30 15A72 16S50 05C83 05C90 PDFBibTeX XMLCite \textit{W. J. Martin}, Linear Algebra Appl. 619, 50--106 (2021; Zbl 1462.05362) Full Text: DOI
Iqbal, Quaid; Koolen, Jack H.; Park, Jongyook; Rehman, Masood Ur Distance-regular graphs with diameter 3 and eigenvalue \(a_2 - c_3\). (English) Zbl 1437.05240 Linear Algebra Appl. 587, 271-290 (2020). MSC: 05E30 05C50 05C12 PDFBibTeX XMLCite \textit{Q. Iqbal} et al., Linear Algebra Appl. 587, 271--290 (2020; Zbl 1437.05240) Full Text: DOI
Dalfó, C. A survey on the missing Moore graph. (English) Zbl 1411.05155 Linear Algebra Appl. 569, 1-14 (2019). MSC: 05C50 05C25 05C12 20B25 20C15 PDFBibTeX XMLCite \textit{C. Dalfó}, Linear Algebra Appl. 569, 1--14 (2019; Zbl 1411.05155) Full Text: DOI Link
Azimi, A.; Bapat, R. B. Moore-Penrose inverse of the incidence matrix of a distance regular graph. (English) Zbl 1418.05067 Linear Algebra Appl. 551, 92-103 (2018). MSC: 05C20 05C50 15A09 PDFBibTeX XMLCite \textit{A. Azimi} and \textit{R. B. Bapat}, Linear Algebra Appl. 551, 92--103 (2018; Zbl 1418.05067) Full Text: DOI
Alazemi, Abdullah; Anđelić, Milica; Koledin, Tamara; Stanić, Zoran Distance-regular graphs with small number of distinct distance eigenvalues. (English) Zbl 1370.05129 Linear Algebra Appl. 531, 83-97 (2017). MSC: 05C50 PDFBibTeX XMLCite \textit{A. Alazemi} et al., Linear Algebra Appl. 531, 83--97 (2017; Zbl 1370.05129) Full Text: DOI
Bang, Sejeong; Koolen, Jack Distance-regular graphs of diameter 3 having eigenvalue \(-1\). (English) Zbl 1370.05130 Linear Algebra Appl. 531, 38-53 (2017). MSC: 05C50 05C12 05E30 PDFBibTeX XMLCite \textit{S. Bang} and \textit{J. Koolen}, Linear Algebra Appl. 531, 38--53 (2017; Zbl 1370.05130) Full Text: DOI
MacLean, Mark S.; Miklavič, Štefko On bipartite distance-regular graphs with exactly two irreducible T-modules with endpoint two. (English) Zbl 1352.05196 Linear Algebra Appl. 515, 275-297 (2017). MSC: 05E30 05C12 PDFBibTeX XMLCite \textit{M. S. MacLean} and \textit{Š. Miklavič}, Linear Algebra Appl. 515, 275--297 (2017; Zbl 1352.05196) Full Text: DOI arXiv
Qiao, Zhi; Koolen, Jack H.; Park, Jongyook 2-walk-regular graphs with a small number of vertices compared to the valency. (English) Zbl 1352.05063 Linear Algebra Appl. 510, 10-24 (2016). MSC: 05C12 05E30 05C50 PDFBibTeX XMLCite \textit{Z. Qiao} et al., Linear Algebra Appl. 510, 10--24 (2016; Zbl 1352.05063) Full Text: DOI
Aalipour, Ghodratollah; Abiad, Aida; Berikkyzy, Zhanar; Cummings, Jay; De Silva, Jessica; Gao, Wei; Heysse, Kristin; Hogben, Leslie; Kenter, Franklin H. J.; Lin, Jephian C.-H.; Tait, Michael On the distance spectra of graphs. (English) Zbl 1331.05131 Linear Algebra Appl. 497, 66-87 (2016). MSC: 05C50 05C12 05C31 05E30 15A15 15A18 15B48 15B57 PDFBibTeX XMLCite \textit{G. Aalipour} et al., Linear Algebra Appl. 497, 66--87 (2016; Zbl 1331.05131) Full Text: DOI arXiv
MacLean, Mark S.; Miklavič, Štefko; Penjić, Safet On the Terwilliger algebra of bipartite distance-regular graphs with \(\Delta_{2}=0\) and \(c_{2}=1\). (English) Zbl 1331.05237 Linear Algebra Appl. 496, 307-330 (2016). MSC: 05E30 05C50 05C12 PDFBibTeX XMLCite \textit{M. S. MacLean} et al., Linear Algebra Appl. 496, 307--330 (2016; Zbl 1331.05237) Full Text: DOI
Fiol, M. A. Quotient-polynomial graphs. (English) Zbl 1326.05174 Linear Algebra Appl. 488, 363-376 (2016). MSC: 05E30 05E05 05C50 05C12 42C05 PDFBibTeX XMLCite \textit{M. A. Fiol}, Linear Algebra Appl. 488, 363--376 (2016; Zbl 1326.05174) Full Text: DOI arXiv
Coutinho, G.; Godsil, C.; Shirazi, H.; Zhan, H. Equiangular lines and covers of the complete graph. (English) Zbl 1409.05220 Linear Algebra Appl. 488, 264-283 (2016). MSC: 05E30 15B33 42C15 PDFBibTeX XMLCite \textit{G. Coutinho} et al., Linear Algebra Appl. 488, 264--283 (2016; Zbl 1409.05220) Full Text: DOI arXiv
Liu, Huan; Hou, Bo; Gao, Suogang Leonard triples, the Racah algebra, and some distance-regular graphs of Racah type. (English) Zbl 1325.05185 Linear Algebra Appl. 484, 435-456 (2015). MSC: 05E30 05C12 15A04 33D45 PDFBibTeX XMLCite \textit{H. Liu} et al., Linear Algebra Appl. 484, 435--456 (2015; Zbl 1325.05185) Full Text: DOI
Brouwer, A. E.; Fiol, M. A. Distance-regular graphs where the distance-\(d\) graph has fewer distinct eigenvalues. (English) Zbl 1314.05053 Linear Algebra Appl. 480, 115-126 (2015). MSC: 05C12 05E30 05C50 PDFBibTeX XMLCite \textit{A. E. Brouwer} and \textit{M. A. Fiol}, Linear Algebra Appl. 480, 115--126 (2015; Zbl 1314.05053) Full Text: DOI arXiv
Atik, Fouzul; Panigrahi, Pratima On the distance spectrum of distance regular graphs. (English) Zbl 1312.05077 Linear Algebra Appl. 478, 256-273 (2015). MSC: 05C50 05C12 PDFBibTeX XMLCite \textit{F. Atik} and \textit{P. Panigrahi}, Linear Algebra Appl. 478, 256--273 (2015; Zbl 1312.05077) Full Text: DOI
Coutinho, G.; Godsil, C.; Guo, K.; Vanhove, F. Perfect state transfer on distance-regular graphs and association schemes. (English) Zbl 1312.05147 Linear Algebra Appl. 478, 108-130 (2015). MSC: 05E30 05C81 15A16 81P68 PDFBibTeX XMLCite \textit{G. Coutinho} et al., Linear Algebra Appl. 478, 108--130 (2015; Zbl 1312.05147) Full Text: DOI arXiv
Gavrilyuk, Alexander L.; Koolen, Jack H. The Terwilliger polynomial of a \(Q\)-polynomial distance-regular graph and its application to pseudo-partition graphs. (English) Zbl 1303.05214 Linear Algebra Appl. 466, 117-140 (2015). MSC: 05E30 05C31 05C12 PDFBibTeX XMLCite \textit{A. L. Gavrilyuk} and \textit{J. H. Koolen}, Linear Algebra Appl. 466, 117--140 (2015; Zbl 1303.05214) Full Text: DOI arXiv
van Dam, E. R.; Fiol, M. A. The Laplacian spectral excess theorem for distance-regular graphs. (English) Zbl 1296.05208 Linear Algebra Appl. 458, 245-250 (2014). MSC: 05E30 05C50 05C12 42C05 PDFBibTeX XMLCite \textit{E. R. van Dam} and \textit{M. A. Fiol}, Linear Algebra Appl. 458, 245--250 (2014; Zbl 1296.05208) Full Text: DOI arXiv
Hanson, Edward A characterization of bipartite Leonard pairs using the notion of a tail. (English) Zbl 1391.15045 Linear Algebra Appl. 452, 46-67 (2014). MSC: 15A21 15A03 05E30 PDFBibTeX XMLCite \textit{E. Hanson}, Linear Algebra Appl. 452, 46--67 (2014; Zbl 1391.15045) Full Text: DOI arXiv
Lee, Guang-Siang; Weng, Chih-wen A characterization of bipartite distance-regular graphs. (English) Zbl 1292.05173 Linear Algebra Appl. 446, 91-103 (2014). MSC: 05C50 05E30 PDFBibTeX XMLCite \textit{G.-S. Lee} and \textit{C.-w. Weng}, Linear Algebra Appl. 446, 91--103 (2014; Zbl 1292.05173) Full Text: DOI
Lee, Jae-Ho \(Q\)-polynomial distance-regular graphs and a double affine Hecke algebra of rank one. (English) Zbl 1282.05221 Linear Algebra Appl. 439, No. 10, 3184-3240 (2013). MSC: 05E30 20C08 33D80 PDFBibTeX XMLCite \textit{J.-H. Lee}, Linear Algebra Appl. 439, No. 10, 3184--3240 (2013; Zbl 1282.05221) Full Text: DOI arXiv
Cámara, Marc; van Dam, Edwin R.; Koolen, Jack H.; Park, Jongyook Geometric aspects of 2-walk-regular graphs. (English) Zbl 1282.05215 Linear Algebra Appl. 439, No. 9, 2692-2710 (2013). MSC: 05E30 05C50 PDFBibTeX XMLCite \textit{M. Cámara} et al., Linear Algebra Appl. 439, No. 9, 2692--2710 (2013; Zbl 1282.05215) Full Text: DOI arXiv
Hanson, Edward A characterization of Leonard pairs using the parameters \(\{a_i\}^d_{i=0}\). (English) Zbl 1266.15018 Linear Algebra Appl. 438, No. 5, 2289-2305 (2013). Reviewer: C. M. da Fonseca (Coimbra) MSC: 15A21 05E30 05C50 PDFBibTeX XMLCite \textit{E. Hanson}, Linear Algebra Appl. 438, No. 5, 2289--2305 (2013; Zbl 1266.15018) Full Text: DOI arXiv
Bang, S. Geometric distance-regular graphs without 4-claws. (English) Zbl 1257.05031 Linear Algebra Appl. 438, No. 1, 37-46 (2013). MSC: 05C12 05C50 05C69 PDFBibTeX XMLCite \textit{S. Bang}, Linear Algebra Appl. 438, No. 1, 37--46 (2013; Zbl 1257.05031) Full Text: DOI arXiv
Fiol, M. A. Pseudo-distance-regularized graphs are distance-regular or distance-biregular. (English) Zbl 1251.05045 Linear Algebra Appl. 437, No. 12, 2973-2977 (2012). MSC: 05C12 PDFBibTeX XMLCite \textit{M. A. Fiol}, Linear Algebra Appl. 437, No. 12, 2973--2977 (2012; Zbl 1251.05045) Full Text: DOI arXiv
Hanson, Edward A characterization of Leonard pairs using the notion of a tail. (English) Zbl 1232.15002 Linear Algebra Appl. 435, No. 11, 2961-2970 (2011). Reviewer: Nicholas Karampetakis (Thessaloniki) MSC: 15A04 15A21 05E30 PDFBibTeX XMLCite \textit{E. Hanson}, Linear Algebra Appl. 435, No. 11, 2961--2970 (2011; Zbl 1232.15002) Full Text: DOI arXiv
Dalfó, C.; van Dam, E. R.; Fiol, M. A. On perturbations of almost distance-regular graphs. (English) Zbl 1222.05152 Linear Algebra Appl. 435, No. 10, 2626-2638 (2011). MSC: 05C50 05E30 PDFBibTeX XMLCite \textit{C. Dalfó} et al., Linear Algebra Appl. 435, No. 10, 2626--2638 (2011; Zbl 1222.05152) Full Text: DOI arXiv
Koolen, Jack H.; Yu, Hyonju The distance-regular graphs such that all of its second largest local eigenvalues are at most one. (English) Zbl 1222.05163 Linear Algebra Appl. 435, No. 10, 2507-2519 (2011). MSC: 05C50 PDFBibTeX XMLCite \textit{J. H. Koolen} and \textit{H. Yu}, Linear Algebra Appl. 435, No. 10, 2507--2519 (2011; Zbl 1222.05163) Full Text: DOI arXiv
Koolen, Jack H.; Park, Jongyook; Yu, Hyonju An inequality involving the second largest and smallest eigenvalue of a distance-regular graph. (English) Zbl 1226.05159 Linear Algebra Appl. 434, No. 12, 2404-2412 (2011). MSC: 05C50 15A42 PDFBibTeX XMLCite \textit{J. H. Koolen} et al., Linear Algebra Appl. 434, No. 12, 2404--2412 (2011; Zbl 1226.05159) Full Text: DOI arXiv
Dalfó, C.; Fiol, M. A.; Garriga, E. Characterizing \((\ell ,m)\)-walk-regular graphs. (English) Zbl 1213.05164 Linear Algebra Appl. 433, No. 11-12, 1821-1826 (2010). MSC: 05C50 05C12 05E30 PDFBibTeX XMLCite \textit{C. Dalfó} et al., Linear Algebra Appl. 433, No. 11--12, 1821--1826 (2010; Zbl 1213.05164) Full Text: DOI
Cerzo, Diana R. Structure of thin irreducible modules of a \(Q\)-polynomial distance-regular graph. (English) Zbl 1226.05265 Linear Algebra Appl. 433, No. 8-10, 1573-1613 (2010). MSC: 05E30 05C12 PDFBibTeX XMLCite \textit{D. R. Cerzo}, Linear Algebra Appl. 433, No. 8--10, 1573--1613 (2010; Zbl 1226.05265) Full Text: DOI arXiv
Fiol, M. A.; Gago, S.; Garriga, E. A simple proof of the spectral excess theorem for distance-regular graphs. (English) Zbl 1221.05112 Linear Algebra Appl. 432, No. 9, 2418-2422 (2010). MSC: 05C12 PDFBibTeX XMLCite \textit{M. A. Fiol} et al., Linear Algebra Appl. 432, No. 9, 2418--2422 (2010; Zbl 1221.05112) Full Text: DOI
Tanaka, Hajime A bilinear form relating two Leonard systems. (English) Zbl 1228.05320 Linear Algebra Appl. 431, No. 10, 1726-1739 (2009). MSC: 05E30 05E10 33C45 33D45 PDFBibTeX XMLCite \textit{H. Tanaka}, Linear Algebra Appl. 431, No. 10, 1726--1739 (2009; Zbl 1228.05320) Full Text: DOI arXiv
Miklavič, Štefko The Terwilliger algebra of a distance-regular graph of negative type. (English) Zbl 1225.05257 Linear Algebra Appl. 430, No. 1, 251-270 (2009). MSC: 05E30 05C12 PDFBibTeX XMLCite \textit{Š. Miklavič}, Linear Algebra Appl. 430, No. 1, 251--270 (2009; Zbl 1225.05257) Full Text: DOI arXiv
Bang, Sejeong; van Dam, Edwin R.; Koolen, Jack H. Spectral characterization of the Hamming graphs. (English) Zbl 1152.05041 Linear Algebra Appl. 429, No. 11-12, 2678-2686 (2008). Reviewer: Mirko Lepović (Kragujevac) MSC: 05C50 05E30 PDFBibTeX XMLCite \textit{S. Bang} et al., Linear Algebra Appl. 429, No. 11--12, 2678--2686 (2008; Zbl 1152.05041) Full Text: DOI Link
Fiol, M. A.; Gimbert, J.; Miller, M. Multipartite Moore digraphs. (English) Zbl 1105.05028 Linear Algebra Appl. 419, No. 1, 234-250 (2006). MSC: 05C20 05C50 05E30 PDFBibTeX XMLCite \textit{M. A. Fiol} et al., Linear Algebra Appl. 419, No. 1, 234--250 (2006; Zbl 1105.05028) Full Text: DOI
Fiol, M. A. Spectral bounds and distance-regularity. (English) Zbl 1060.05102 Linear Algebra Appl. 397, 17-33 (2005). MSC: 05E30 05E35 PDFBibTeX XMLCite \textit{M. A. Fiol}, Linear Algebra Appl. 397, 17--33 (2005; Zbl 1060.05102) Full Text: DOI
Brouwer, Andries E.; Haemers, Willem H. Eigenvalues and perfect matchings. (English) Zbl 1056.05097 Linear Algebra Appl. 395, 155-162 (2005). MSC: 05C50 05C70 05E30 PDFBibTeX XMLCite \textit{A. E. Brouwer} and \textit{W. H. Haemers}, Linear Algebra Appl. 395, 155--162 (2005; Zbl 1056.05097) Full Text: DOI Link
van Dam, Edwin R.; Haemers, Willem H. Which graphs are determined by their spectrum? (English) Zbl 1026.05079 Linear Algebra Appl. 373, 241-272 (2003). MSC: 05C50 05E30 PDFBibTeX XMLCite \textit{E. R. van Dam} and \textit{W. H. Haemers}, Linear Algebra Appl. 373, 241--272 (2003; Zbl 1026.05079) Full Text: DOI
Terwilliger, Paul The subconstituent algebra of a distance-regular graph; thin modules with endpoint one. (English) Zbl 1011.05066 Linear Algebra Appl. 356, No. 1-3, 157-187 (2002). Reviewer: Alexandre A.Makhnev (Ekaterinburg) MSC: 05E30 05E35 05C50 PDFBibTeX XMLCite \textit{P. Terwilliger}, Linear Algebra Appl. 356, No. 1--3, 157--187 (2002; Zbl 1011.05066) Full Text: DOI
Li, Feng-gao; Wang, Yang-xian Subconstituents of dual polar graph in finite classical space. III. (English) Zbl 0999.05072 Linear Algebra Appl. 349, No. 1-3, 105-123 (2002). MSC: 05C50 05E30 51D20 15A99 PDFBibTeX XMLCite \textit{F.-g. Li} and \textit{Y.-x. Wang}, Linear Algebra Appl. 349, No. 1--3, 105--123 (2002; Zbl 0999.05072) Full Text: DOI
Pascasio, Arlene A. An inequality on the cosines of a tight distance-regular graph. (English) Zbl 0979.05112 Linear Algebra Appl. 325, No. 1-3, 147-159 (2001). Reviewer: Nikolai L.Manev (Sofia) MSC: 05E30 PDFBibTeX XMLCite \textit{A. A. Pascasio}, Linear Algebra Appl. 325, No. 1--3, 147--159 (2001; Zbl 0979.05112) Full Text: DOI
Fiol, M. A. On pseudo-distance-regularity. (English) Zbl 0978.05050 Linear Algebra Appl. 323, No. 1-3, 145-165 (2001). Reviewer: Dragoš Cvetković (Beograd) MSC: 05C50 PDFBibTeX XMLCite \textit{M. A. Fiol}, Linear Algebra Appl. 323, No. 1--3, 145--165 (2001; Zbl 0978.05050) Full Text: DOI
de Caen, D. Degree of indecomposability of certain highly regular zero-one matrices. (English) Zbl 0864.15008 Linear Algebra Appl. 247, 151-158 (1996). Reviewer: N.J.Pullman (Kingston/Ontario) MSC: 15B36 05B20 05C50 PDFBibTeX XMLCite \textit{D. de Caen}, Linear Algebra Appl. 247, 151--158 (1996; Zbl 0864.15008) Full Text: DOI
Haemers, Willem H. Distance-regularity and the spectrum of graphs. (English) Zbl 0845.05101 Linear Algebra Appl. 236, 265-278 (1996). Reviewer: Liu Zhenhong (Beijing) MSC: 05E30 05C50 05C12 PDFBibTeX XMLCite \textit{W. H. Haemers}, Linear Algebra Appl. 236, 265--278 (1996; Zbl 0845.05101) Full Text: DOI Link
Godsil, C. D.; Koolen, J. H. On the multiplicity of eigenvalues of distance-regular graphs. (English) Zbl 0832.05075 Linear Algebra Appl. 226-228, 273-275 (1995). Reviewer: J.E.Graver (Syracuse) MSC: 05C50 PDFBibTeX XMLCite \textit{C. D. Godsil} and \textit{J. H. Koolen}, Linear Algebra Appl. 226--228, 273--275 (1995; Zbl 0832.05075) Full Text: DOI
Higman, D. C. Rank 5 association schemes and triality. (English) Zbl 0832.05099 Linear Algebra Appl. 226-228, 197-222 (1995). Reviewer: V.A.Ufnarovski (Lund) MSC: 05E30 05E15 05E20 PDFBibTeX XMLCite \textit{D. C. Higman}, Linear Algebra Appl. 226--228, 197--222 (1995; Zbl 0832.05099) Full Text: DOI
van Dam, Edwin R. Regular graphs with four eigenvalues. (English) Zbl 0839.05072 Linear Algebra Appl. 226-228, 139-162 (1995). Reviewer: W.K.Chen (Chicago) MSC: 05C50 05C75 05E30 PDFBibTeX XMLCite \textit{E. R. van Dam}, Linear Algebra Appl. 226--228, 139--162 (1995; Zbl 0839.05072) Full Text: DOI Backlinks: MO
Weichsel, Paul M. Distance-regular graphs in block form. (English) Zbl 0715.05051 Linear Algebra Appl. 126, 135-148 (1989). MSC: 05C50 PDFBibTeX XMLCite \textit{P. M. Weichsel}, Linear Algebra Appl. 126, 135--148 (1989; Zbl 0715.05051) Full Text: DOI
Weichsel, Paul M. Polynomials on graphs. (English) Zbl 0644.05037 Linear Algebra Appl. 93, 179-186 (1987). Reviewer: D.Cvetkovic MSC: 05C50 05C25 PDFBibTeX XMLCite \textit{P. M. Weichsel}, Linear Algebra Appl. 93, 179--186 (1987; Zbl 0644.05037) Full Text: DOI
Mohar, Bojan; Omladič, Matjaž Divisors and the spectrum of infinite graphs. (English) Zbl 0615.05041 Linear Algebra Appl. 91, 99-106 (1987). MSC: 05C50 05C99 PDFBibTeX XMLCite \textit{B. Mohar} and \textit{M. Omladič}, Linear Algebra Appl. 91, 99--106 (1987; Zbl 0615.05041) Full Text: DOI
Ito, Tatsuro Bipartite distance-regular graphs of valency three. (English) Zbl 0501.05052 Linear Algebra Appl. 46, 195-213 (1982). MSC: 05C75 PDFBibTeX XMLCite \textit{T. Ito}, Linear Algebra Appl. 46, 195--213 (1982; Zbl 0501.05052) Full Text: DOI
Godsil, C. D.; McKay, B. D. Feasibility conditions for the existence of walk-regular graphs. (English) Zbl 0452.05045 Linear Algebra Appl. 30, 51-61 (1980). MSC: 05C50 PDFBibTeX XMLCite \textit{C. D. Godsil} and \textit{B. D. McKay}, Linear Algebra Appl. 30, 51--61 (1980; Zbl 0452.05045) Full Text: DOI