Number of Spanning trees in Different Products of Complete and Complete Tripartite Graphs

摘要

Many models in engineering have regular patterns and can be viewed as the product of a number of simple graphs. These subgraphs, which are used in the formation of a model, are called the generators of that model. In this paper simple explicit formulae are derived for calculating the complexity of some products of compete and complete tripartite graphs such as: Cartesian product, Normal product, Composition product, Tensor product, Symmetric product, and Strong sum, by an extension of Kirchhoff's formula, using techniques from linear algebra and matrix theory.