Let k be a natural number and let G be a graph with at least k vertices. A.E. Brouwer conjectured that the sum of the k largest Laplacian eigenvalues of G is at most e(G) (k choose 2), where e(G) is the number of edges of G. We prove this conjecture for k = 2. We also show that if G is a tree,...

In this report, we discuss the use of Petri Net language theory for business process modeling. Essentially, the focus is on the opportunities of the modeling technique for analysis and verification. Semantic compatibility, as opposed to syntactic compatibility, is concerned with the...

We consider k-regular graphs with loops, and study the Lovasz O-numbers and Schrijver O-numbers of the graphs that result when the loop edges are removed. We show that the O-number dominates a recent eigenvalue upper bound on the stability number due to Godsil and Newman [C.D. Godsil and M.W....

Multiobjective shortest path problems are computationally harder than single objective ones. In particular, execution time is an important limiting factor in exact multiobjective search algorithms. This paper explores the possibility of improving search performance in those cases where the...

This paper addresses a bicriteria no-wait flow-shop scheduling problem with multiple robots transferring jobs between pairs of consecutive machines. The robots share an identical track positioned alongside the machine transfer line. Each robot is assigned to a portion of the tract from which it...