Deaett, Louis; Fallat, Shaun; Furst, Veronika; Hutchens, John; Mitchell, Lon; Zhang, Yaqi Sparks of symmetric matrices and their graphs. (English) Zbl 07807938 Electron. J. Linear Algebra 39, 591-606 (2023). MSC: 05C50 15A18 15A29 PDFBibTeX XMLCite \textit{L. Deaett} et al., Electron. J. Linear Algebra 39, 591--606 (2023; Zbl 07807938) Full Text: DOI
Allem, L. Emilio; Braga, Rodrigo O.; Hoppen, Carlos; Oliveira, Elismar R.; Sibemberg, Lucas S.; Trevisan, Vilmar Diminimal families of arbitrary diameter. (English) Zbl 1520.05060 Linear Algebra Appl. 676, 318-351 (2023). MSC: 05C50 05C12 05C35 05C05 15A29 PDFBibTeX XMLCite \textit{L. E. Allem} et al., Linear Algebra Appl. 676, 318--351 (2023; Zbl 1520.05060) Full Text: DOI arXiv
Boyko, O. P.; Martynyuk, O. M.; Pivovarchik, V. M. Upper bound for the diameter of a tree in the quantum graph theory. (English. Ukrainian original) Zbl 1521.81091 Ukr. Math. J. 74, No. 8, 1165-1174 (2023); translation from Ukr. Mat. Zh. 74, No. 8, 1020-1028 (2022). MSC: 81Q35 05C12 34B24 05C05 47A10 35P20 PDFBibTeX XMLCite \textit{O. P. Boyko} et al., Ukr. Math. J. 74, No. 8, 1165--1174 (2023; Zbl 1521.81091); translation from Ukr. Mat. Zh. 74, No. 8, 1020--1028 (2022) Full Text: DOI
Pivovarchik, Vyacheslav; Wei, Guangsheng; Yang, Lu On multiplicities of eigenvalues of a spectral problem on a prolate tree. (English) Zbl 1507.34021 Oper. Matrices 16, No. 3, 685-695 (2022). MSC: 34A55 39A70 70F17 70J30 PDFBibTeX XMLCite \textit{V. Pivovarchik} et al., Oper. Matrices 16, No. 3, 685--695 (2022; Zbl 1507.34021) Full Text: DOI
Johnson, Charles R.; Wakhare, Tanay The inverse eigenvalue problem for linear trees. (English) Zbl 1483.15008 Discrete Math. 345, No. 4, Article ID 112737, 17 p. (2022). MSC: 15A29 15A18 05C50 05C05 PDFBibTeX XMLCite \textit{C. R. Johnson} and \textit{T. Wakhare}, Discrete Math. 345, No. 4, Article ID 112737, 17 p. (2022; Zbl 1483.15008) Full Text: DOI arXiv
Kenter, Franklin H. J.; Lin, Jephian C.-H. A zero forcing technique for bounding sums of eigenvalue multiplicities. (English) Zbl 1471.05058 Linear Algebra Appl. 629, 138-167 (2021). MSC: 05C50 05C57 15A29 15A42 90C10 PDFBibTeX XMLCite \textit{F. H. J. Kenter} and \textit{J. C. H. Lin}, Linear Algebra Appl. 629, 138--167 (2021; Zbl 1471.05058) Full Text: DOI arXiv
Johnson, Charles R.; Saiago, Carlos M.; Toyonaga, Kenji Change in vertex status after removal of another vertex in the general setting. (English) Zbl 1476.15015 Linear Algebra Appl. 612, 128-145 (2021). Reviewer: Shariefuddin Pirzada (Srinagar) MSC: 15A18 05B20 05C50 PDFBibTeX XMLCite \textit{C. R. Johnson} et al., Linear Algebra Appl. 612, 128--145 (2021; Zbl 1476.15015) Full Text: DOI
Pivovarchik, V. N. On the minimum number of distinct eigenvalues in the problem for a tree formed by Stieltjes strings. (English. Ukrainian original) Zbl 1448.05133 Ukr. Math. J. 72, No. 1, 149-156 (2020); translation from Ukr. Mat. Zh. 72, No. 1, 135-141 (2020). MSC: 05C50 05C35 05C05 05C12 05C38 PDFBibTeX XMLCite \textit{V. N. Pivovarchik}, Ukr. Math. J. 72, No. 1, 149--156 (2020; Zbl 1448.05133); translation from Ukr. Mat. Zh. 72, No. 1, 135--141 (2020) Full Text: DOI
Barrett, Wayne; Butler, Steve; Fallat, Shaun M.; Hall, H. Tracy; Hogben, Leslie; Lin, Jephian C.-H.; Shader, Bryan L.; Young, Michael The inverse eigenvalue problem of a graph: multiplicities and minors. (English) Zbl 1436.05059 J. Comb. Theory, Ser. B 142, 276-306 (2020). MSC: 05C50 05C83 15A18 15A29 PDFBibTeX XMLCite \textit{W. Barrett} et al., J. Comb. Theory, Ser. B 142, 276--306 (2020; Zbl 1436.05059) Full Text: DOI arXiv
Saiago, Carlos M. Diagonalizable matrices whose graph is a tree: the minimum number of distinct eigenvalues and the feasibility of eigenvalue assignments. (English) Zbl 1433.15014 Spec. Matrices 7, 316-326 (2019). MSC: 15A18 05C05 05C50 PDFBibTeX XMLCite \textit{C. M. Saiago}, Spec. Matrices 7, 316--326 (2019; Zbl 1433.15014) Full Text: DOI
Adm, Mohammad; Fallat, Shaun M. The maximum multiplicity of the largest \(k\)-th eigenvalue in a matrix whose graph is acyclic or unicyclic. (English) Zbl 1417.05116 Discrete Math. 342, No. 10, 2924-2950 (2019). MSC: 05C50 05B20 PDFBibTeX XMLCite \textit{M. Adm} and \textit{S. M. Fallat}, Discrete Math. 342, No. 10, 2924--2950 (2019; Zbl 1417.05116) Full Text: DOI
Ferrero, Daniela; Flagg, Mary; Hall, H. Tracy; Hogben, Leslie; Lin, Jephian C.-H.; Meyer, Seth A.; Nasserasr, Shahla; Shader, Bryan Rigid linkages and partial zero forcing. (English) Zbl 1416.05171 Electron. J. Comb. 26, No. 2, Research Paper P2.43, 25 p. (2019). MSC: 05C50 15A18 15B57 PDFBibTeX XMLCite \textit{D. Ferrero} et al., Electron. J. Comb. 26, No. 2, Research Paper P2.43, 25 p. (2019; Zbl 1416.05171) Full Text: arXiv Link
Barrett, Wayne; Fallat, Shaun; Hall, H. Tracy; Hogben, Leslie; Lin, Jephian C.-H.; Shader, Bryan L. Generalizations of the strong Arnold property and the minimum number of distinct eigenvalues of a graph. (English) Zbl 1366.05065 Electron. J. Comb. 24, No. 2, Research Paper P2.40, 28 p. (2017). MSC: 05C50 15A18 15A29 15B57 58C15 PDFBibTeX XMLCite \textit{W. Barrett} et al., Electron. J. Comb. 24, No. 2, Research Paper P2.40, 28 p. (2017; Zbl 1366.05065) Full Text: arXiv Link
Buckley, Shannon P.; Corliss, Joseph G.; Johnson, Charles R.; Araúz Lombardía, Cristina; Saiago, Carlos M. Questions, conjectures, and data about multiplicity lists for trees. (English) Zbl 1350.05092 Linear Algebra Appl. 511, 72-109 (2016). MSC: 05C50 05C05 15A18 PDFBibTeX XMLCite \textit{S. P. Buckley} et al., Linear Algebra Appl. 511, 72--109 (2016; Zbl 1350.05092) Full Text: DOI
Johnson, Charles R.; Li, Andrew A.; Walker, Andrew J. Ordered multiplicity lists for eigenvalues of symmetric matrices whose graph is a linear tree. (English) Zbl 1298.05068 Discrete Math. 333, 39-55 (2014). MSC: 05C05 05C07 PDFBibTeX XMLCite \textit{C. R. Johnson} et al., Discrete Math. 333, 39--55 (2014; Zbl 1298.05068) Full Text: DOI
Kim, In-Jae; Shader, Bryan L. Unordered multiplicity lists of a class of binary trees. (English) Zbl 1280.05079 Linear Algebra Appl. 438, No. 10, 3781-3788 (2013). MSC: 05C50 05C05 05C35 15A18 PDFBibTeX XMLCite \textit{I.-J. Kim} and \textit{B. L. Shader}, Linear Algebra Appl. 438, No. 10, 3781--3788 (2013; Zbl 1280.05079) Full Text: DOI
Kim, In-Jae; Shader, Bryan L. Smith normal form and acyclic matrices. (English) Zbl 1226.05158 J. Algebr. Comb. 29, No. 1, 63-80 (2009). MSC: 05C50 15A21 15A18 PDFBibTeX XMLCite \textit{I.-J. Kim} and \textit{B. L. Shader}, J. Algebr. Comb. 29, No. 1, 63--80 (2009; Zbl 1226.05158) Full Text: DOI arXiv
Fallat, Shaun M.; Hogben, Leslie The minimum rank of symmetric matrices described by a graph: a survey. (English) Zbl 1122.05057 Linear Algebra Appl. 426, No. 2-3, 558-582 (2007). MSC: 05C50 15A03 15A18 PDFBibTeX XMLCite \textit{S. M. Fallat} and \textit{L. Hogben}, Linear Algebra Appl. 426, No. 2--3, 558--582 (2007; Zbl 1122.05057) Full Text: DOI arXiv
Barioli, Francesco; Fallat, Shaun; Hogben, Leslie Computation of minimal rank and path cover number for certain graphs. (English) Zbl 1052.05045 Linear Algebra Appl. 392, 289-303 (2004). MSC: 05C50 15A18 PDFBibTeX XMLCite \textit{F. Barioli} et al., Linear Algebra Appl. 392, 289--303 (2004; Zbl 1052.05045) Full Text: DOI