Commutative algebra and graph theory are two vibrant areas of mathematics that have grown increasingly interrelated. At this interface, algebraic methods are applied to study combinatorial structures, ...

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Abstract: Nested codes have been employed in a large number of communication applications as a specific case of superposition codes, for example to implement binning schemes in the presence of noise, ...

Abstract: The second smallest eigenvalue of the Laplacian matrix, also known as the algebraic connectivity, characterizes the performance of some dynamic processes on networks, such as consensus in ...

A lot of combinatorial objects have a natural bialgebra structure. In this paper, we prove that the vector space spanned by labeled simple graphs is a bialgebra with the conjunction product and the ...

A project headed by the SEI’s Scott McMillan took a step in 2020 toward standardizing graph algorithm application development in C++. The GraphBLAS, Basic Linear Algebra Subprograms for Graphs, is a ...

There has recently been impressive progress—after nearly 50 years of stagnation—in algorithms that find solutions for certain hard computational problems, including the famous Hamiltonian problem.

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