02560nam a22003137a 4500 58629 58629 20211130113232.0 211130b ||||| |||| 00| 0 eng d 9781470437220 :Variety Books Publishers & Distributors :B-10 Street No 2 West Vinod Nagar Delhi 110092 :IM2893 :25/11/2021 511.55 BRU Brualdi, Richard A. The Mutually Beneficial Relationship of Graphs and Matrices / Richard A Brualdi New Delhi :University Press 2017 ix, 96 pages : illustrations ; 26 cm. 985 Regional conference series in mathematics, no. 115. Machine generated contents note: 1.1.Nonnegative Matrices -- 1.2.Symmetric Matrices -- Bibliography -- 2.1.Some Basic Properties -- 2.2.Eigenvalues and Graph Parameters -- 2.3.Graphs with small Amax -- 2.4.Laplacian Matrix of a Graph -- Bibliography -- 3.1.Rado-Hall Theorem -- 3.2.Applications -- Bibliography -- 4.1.Motivation and Definition -- 4.2.Colin de Verdiere Number and Graph Properties -- Bibliography -- 5.1.Equivalent Formulations -- 5.2.The Classes A(R, S) -- 5.3.A Generalization -- Bibliography -- 6.1.Sign-Nonsingular Matrices -- 6.2.An Application -- 6.3.Spectrally Arbitrary Sign Patterns -- Bibliography -- 7.1.Some Classical Theorems -- 7.2.Diagonal Products and Nonsingularity -- Bibliography -- 8.1.Landau's Theorem -- 8.2.A Special Tournament in T(R) -- 8.3.Eigenvalues of Tournament Matrices -- Bibliography -- 9.1.The Doubly Stochastic Polytope -- 9.2.Alternating Sign Matrices -- 9.3.The Alternating Sign Matrix Polytope -- 9.4.ASM Patterns -- Bibliography Note continued: 10.1.(0, 1)-matrices with all Eigenvalues Positive -- 10.2.Totally Nonnegative Matrices -- 10.3.Totally Nonnegative (0, 1)-matrices -- Bibliography Graphs and matrices enjoy a fascinating and mutually beneficial relationship. This interplay has benefited both graph theory and linear algebra. This is not a comprehensive study of graphs and matrices, instead the contributions have been chosen for their accessibility, beauty, and current relevance, and for the possibility of enticing the audience to want to learn more Mathematics General principles of mathematics Matrices. Graph theory. Algebras, Linear. Combinatorial analysis. Matrix Number Theory Brualdi, Richard A. MDL 0 0 ddc 0 1 MDL SNUL 2021-11-30 Variety Books Publishers & Distributors 985.00 0 511.55 BRU M311 2021-11-30 00:00:00 2021-11-30 MDL FPDA Grant