Portale di Ateneo - En.Unibs.it

Graphoids and graphs.
General notions. Topological graphoids. Basic terminology. Basic relations. Subgraphoids and subgraphs. Operations. Connected graphoids. Node/edge sequences of a graph. Noteworthy graphoids and graphs. Path- and mesh-connected graphs, hinged graphs. Noteworthy anodal subgraphoids of a graph. Forest and coforest of a graph. Expansions. Complete and multi-partite graphs. Euler's and Kuratowski's theorems. Oriented graphoids. Digraphs. Fundamental loops and cutsets of a digraph. Meshes.

Revisited Kirchhoff model.
Natural graph of a circuit. Kirchhoff Laws on the natural graph. Voltage and current analysis by graphs. Tellegen theorem revisited.

Laplacian components.
Classic and distributional laplace components in the t and s domains.

Analysis methods.
Tableau, tree, co-tree, semi-topological and mesh methods.

State space methods.
Order of complexity and degeneracy. Topological degeneration indexes. Analysis methods: substitution, normal forest/coforest, multiports. Further degeneration conditions.