6 research outputs found
The Maximum Degree-and-Diameter-Bounded Subgraph in the Mesh
The problem of finding the largest connected subgraph of a given undirected
host graph, subject to constraints on the maximum degree and the
diameter , was introduced in \cite{maxddbs}, as a generalization of the
Degree-Diameter Problem. A case of special interest is when the host graph is a
common parallel architecture. Here we discuss the case when the host graph is a
-dimensional mesh. We provide some general bounds for the order of the
largest subgraph in arbitrary dimension , and for the particular cases of
and , we give constructions that result in
sharper lower bounds.Comment: accepted, 18 pages, 7 figures; Discrete Applied Mathematics, 201
Complete Presentations of Direct Products of Groups
Complete presentations provide a natural solution to the word problem in monoids and groups. Here we give a simple way to construct complete presentations for the direct product of groups, when such presentations are available for the factors. Actually, the construction we are referring to is just the classical construction for direct products of groups, which has been known for a long time, but whose completeness-preserving properties had not been detected. Using this result and some known facts about Coxeter groups, we sketch an algorithm to obtain the complete presentation of any finite Coxeter group. A similar application to Abelian and Hamiltonian groups is mentioned
Complete Presentations of Direct Products of Groups
Complete presentations provide a natural solution to the word problem in monoids and groups. Here we give a simple way to construct complete presentations for the direct product of groups, when such presentations are available for the factors. Actually, the construction we are referring to is just the classical construction for direct products of groups, which has been known for a long time, but whose completeness-preserving properties had not been detected. Using this result and some known facts about Coxeter groups, we sketch an algorithm to obtain the complete presentation of any finite Coxeter group. A similar application to Abelian and Hamiltonian groups is mentioned