The Word Problem and Related Results for Graph Product Groups
نویسنده
چکیده
A graph product is the fundamental group of a graph of groups. Amongst the simplest examples are HNN groups and free products with amalgamation. The torsion and conjugacy theorems are proved for any group presented as a graph product. The graphs over which some graph product has a solvable word problem are characterised. Conditions are then given for the solvability of the word and order problems and also for the extended word problem for cyclic subgroups of any graph product. These results generalise the known ones for HNN groups and free products with amalgamation.
منابع مشابه
Product version of reciprocal degree distance of composite graphs
A {it topological index} of a graph is a real number related to the graph; it does not depend on labeling or pictorial representation of a graph. In this paper, we present the upper bounds for the product version of reciprocal degree distance of the tensor product, join and strong product of two graphs in terms of other graph invariants including the Harary index and Zagreb indices.
متن کاملOn trivial ends of Cayley graph of groups
In this paper, first we introduce the end of locally finite graphs as an equivalence class of infinite paths in the graph. Then we mention the ends of finitely generated groups using the Cayley graph. It was proved that the number of ends of groups are not depended on the Cayley graph and that the number of ends in the groups is equal to zero, one, two, or infinity. For ...
متن کاملAn Effective Method for Utility Preserving Social Network Graph Anonymization Based on Mathematical Modeling
In recent years, privacy concerns about social network graph data publishing has increased due to the widespread use of such data for research purposes. This paper addresses the problem of identity disclosure risk of a node assuming that the adversary identifies one of its immediate neighbors in the published data. The related anonymity level of a graph is formulated and a mathematical model is...
متن کاملCompressed Decision Problems for Graph Products and Applications to (outer) Automorphism Groups
It is shown that the compressed word problem of a graph product of finitely generated groups is polynomial time Turing-reducible to the compressed word problems of the vertex groups. A direct corollary of this result is that the word problem for the automorphism group of a right-angled Artin group or a right-angled Coxeter group can be solved in polynomial time. Moreover, it is shown that a res...
متن کاملA new approach in graph- based integrated production and distribution scheduling for perishable products
This study is concerned with how the quality of perishable products can be improved by shortening the time interval between production and distribution. As special types of food such as dairy products decay fast, the integration of production and distribution scheduling (IPDS) is investigated. An integrated scheduling of both processes improves the performance and costs because the separated sc...
متن کامل