Given a graph G, a dominating set D is a set of vertices such that any vertex not in D has at least one neighbor in D. A {k}-dominating multiset Dk is a multiset of vertices such that any vertex in G has at least k vertices from its closed neighborhood in Dk when counted with multiplicity. In this paper, we utilize the approach developed by Clark and Suen (2000) to prove a ‘‘Vizing-like’’ inequ...

We present in this paper a formalization of multiset relations in the ACL2 theorem prover [6], and we show how multisets can be used to mechanically prove non-trivial termination properties. Every relation on a set A induces a relation on finite multisets over A; it can be shown that the multiset relation induced by a well-founded relation is also wellfounded [3]. We have carried out a mechanic...

Harary’s edge reconstruction conjecture states that a graph G=(V; E) with at least four edges is uniquely determined by the multiset of its edge-deleted subgraphs, i.e. the graphs of the form G − e for e∈E. It is well-known that this multiset uniquely determines the degree sequence of a graph with at least four edges. In this note we generalize this result by showing that the degree sequence of...

This paper describes a rule-based multiset programming paradigm, as a unifying theme for computation. The computations are interpreted as the outcome arising out of deterministic, nondeterministic or stochastic interaction among elements in a multiset object space which includes the environment. These interactions are like chemical reactions and the evolution of the multiset can mimic the biolo...

The following problem is well-known under various forms from car manufacturing and has been presented in Discrete Applied Mathematics(136) by T.Epping, W.Hochstättler and P.Oertel as a combinatorial optimization problem: cars have to be painted in two colors in a sequence where each car occurs twice; assign the two colors to the two occurrences of each car so as to minimize the number of color ...