Betweenness centrality is a distance-based invariant of graphs. In this paper, we use lexicographic product to compute betweenness centrality of some important classes of graphs. Finally, we pose some open problems related to this topic.

In this paper, we introduce a generalization of Hilbert $C^*$-modules which are pre-Finsler modules, namely, $C^{*}$-semi-inner product spaces. Some properties and results of such spaces are investigated, specially the orthogonality in these spaces will be considered. We then study bounded linear operators on $C^{*}$-semi-inner product spaces.

this paper presents an overview of new approaches in rapid product development in production networks from design points of view. the manufacturing industries are changing their focus to global sourcing as a means to improve performance and enhance competitiveness. some partnerships created with this strategy improve product development through collaborative design. with the advent of e-commerc...

This paper develops a model of endogenous product selection by firms. The theory is motivated by new evidence we present on the importance of product switching by U.S. manufacturers. Two-thirds of continuing firms change their product mix every five years, and product switches involve more than 40% of firm output and almost half of existing products. The theoretical model incorporates heterogen...

A Software Product Line (SPL) is a set of related programs. A SPL of a SPL (SPL), or a product line of a product line, is a fundamental scaling of product line concepts. A member of a SPL is not a program, but a SPL. The idea recurses: a SPL is a SPL of a SPL, and so on. The depth of recursion is the rank of the product line. We present an algebra to understand and build feature-based product l...