Graph products with specified domains for configuration processing and formation of the adjacency matrices

Abstract

Purpose

Graph products are extensively used in the analysis and design of regular structures. It is often thought that these products are only applicable to regular graphs. The main aim of this paper is develop new products which are applicable to regular as well and non‐regular structural models.

Design/methodology/approach

New graph products are defined with specified domains. In these products the logical operations of the graph products are only performable in specified domains, and therefore these products can produce configurations which do not need to be regular.

Findings

New graph products are defined and a general theorem is proved for the formation of their adjacency matrices.

Originality/value

The presented graph products overcome the difficulty of employing graph products in structural mechanics, and in particular in space structures. The general theorem of this paper can efficiently be used in the formation of adjacency matrices of the structural models.

Citation

Kaveh, A. and Alinejad, B. (2010), "Graph products with specified domains for configuration processing and formation of the adjacency matrices", Engineering Computations, Vol. 27 No. 2, pp. 205-224. https://doi.org/10.1108/02644401011022373