
We investigate the optimization of a real-world logistics problem, which is concerned with shipping a dangerous chemical substance in various degrees of refinement to several locations and customers. Transport frequencies, inventories, and container flows have to be optimized. On the one hand, we discuss the mathematical structure of our problem (one result being its NP-completeness), and on the other hand, we describe our practical approach, which achieves nearly optimal solutions.
Let
If
The previously studied notions of smart and foolproof finite order domination of a simple graph
Self-dual codes are an important class of linear codes. Hadamard matrices and weighing matrices have been used widely in the construction of binary and ternary self-dual codes. Recently, weighing matrices and orthogonal designs have been used to construct self-dual codes over larger fields. In this paper, we further investigate codes over
We give decomposition formulas of the multiedge and the multipath zeta function of a regular covering of a graph
Let
Every Latin square of prime or prime power order
Two graphs are said to be flow-equivalent if they have the same number of nowhere-zero
The Whitney number
The Picard group is defined as
The domination number of a graph
A fractional automorphism of a graph is a doubly stochastic matrix which commutes with the adjacency matrix of the graph. If we apply an ordinary automorphism to a set of vertices with a particular property, such as being independent or dominating, the resulting set retains that property. We examine the circumstances under which fractional automorphisms preserve the fractional properties of functions on the vertex set.
A king graph
A set
The formula for the number of spanning trees in
For any
is a constant map. For a given graph
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