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Applications of graph theory to matrix theory [PDF]
Proceedings of the American Mathematical Society, 1975 Let A 1 , … , A k {A_1}, \ldots ,{A_k} be n × n n \times n matrices over a commutative ring R R with identity.
Frank W. Owens
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Embedded graph invariants in Chern-Simons theory [PDF]
, 1998 Chern-Simons gauge theory, since its inception as a topological quantum field theory, has proved to be a rich source of understanding for knot invariants.
Alvarez +54 more
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On minimal blocking sets of the generalized quadrangle $Q(4, q)$ [PDF]
Discrete Mathematics & Theoretical Computer Science, 2005 The generalized quadrangle $Q(4,q)$ arising from the parabolic quadric in $PG(4,q)$ always has an ovoid. It is not known whether a minimal blocking set of size smaller than $q^2 + q$ (which is not an ovoid) exists in $Q(4,q)$, $q$ odd. We present results
Miroslava Cimráková, Veerle Fack
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Hadamard matrices of order 36 and double-even self-dual [72,36,12] codes [PDF]
Discrete Mathematics & Theoretical Computer Science, 2005 Before this work, at least 762 inequivalent Hadamard matrices of order 36 were known. We found 7238 Hadamard matrices of order 36 and 522 inequivalent [72,36,12] double-even self-dual codes which are obtained from all 2-(35,17,8) designs with an ...
Iliya Bouyukliev +2 more
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On the enumeration of uniquely reducible double designs [PDF]
Discrete Mathematics & Theoretical Computer Science, 2005 A double $2$-$(v,k,2 \lambda)$ design is a design which is reducible into two $2$-$(v,k,\lambda)$ designs. It is called uniquely reducible if it has, up to equivalence, only one reduction.
Veerle Fack +2 more
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Graph Theory and Algorithms for Network Analysis [PDF]
E3S Web of Conferences, 2023 In network analysis, the study and comprehension of complex systems in numerous fields, such as social networks, transportation networks, and biological networks, are made possible by the crucial role played by graph theory and algorithms.
Arul Sharmila Mary +5 more
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Scattering theory on graphs [PDF]
Journal of Physics A: Mathematical and General, 2001 We consider the scattering theory for the Schr dinger operator $-\Dc_x^2+V(x)$ on graphs made of one-dimensional wires connected to external leads. We derive two expressions for the scattering matrix on arbitrary graphs. One involves matrices that couple arcs (oriented bonds), the other involves matrices that couple vertices.
Texier, Christophe, Montambaux, Gilles
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On (a,d)-antimagic labelings of Hn, FLn and mCn
Indonesian Journal of Combinatorics, 2020 In this paper, we derive the necessary condition for an (a,d )- antimagic labeling of some new classes of graphs such as Hn, F Ln and mCn. We prove that Hn is (7n +2, 1)-antimagic and mCn is ((mn+3)/2,1)- antimagic.
Ramalakshmi Rajendran, K. M. Kathiresan
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