Basic notions from Algebraic and Geometric graph theory. Proof of classic theorems in graph theory. Elements of Combinatorics. Balanced Incomplete Block Designs
To be able to apply the language of Graph Theory to various scientific disciplines,
such as Mathematics,
Physics, Chemistry, Biology, Economics.
Prerequisites
Basic notions of algebra (groups, integers) and Linear Algebra (matrices, eigenvectors, eigenvalues)
Teaching Methods
Blackboard exposition
of definitions examples,
proofs of theorems, with the help of projected color drawings and pictures
Type of Assessment
Four written exams
and an oral
Course program
Definition of a graph. Simple, multiple, oriented graohs. Metric space associated with a graph.
Adjacency matrix. Paths,
trails, walks in a grapoh. Eigenvalues. Degree of a vertex. Formulae involving degres. Degree sequence. Connectedness. Connectivity. Planar graphs. Euler Theorem. Counting theorems. Formula of Cauchy-Frobenius-Burnside. Geometric interpretation of the minimum eigenvalue.
Problem of the three paths of maximum length. Reconstruction Problem for oriented as well as non-oriented graphs. Block designs. Necessary conditions for the exixtence of block designs. Projective planes. Existence problem of projective planes of mixed order