This page discusses key concepts in graph theory, including definitions of walks, trails, and paths, highlighting their distinct characteristics regarding vertex and edge repetition. It explains Euler...This page discusses key concepts in graph theory, including definitions of walks, trails, and paths, highlighting their distinct characteristics regarding vertex and edge repetition. It explains Eulerian trails and Hamiltonian paths and addresses graph connectivity, stating that a graph is connected if any vertex pair has a connecting path. Additionally, it introduces \(n\)-connected graphs and includes practice checkpoints to reinforce understanding of these concepts.
We did quite a few examples that showed how combinatorial properties of arrangements counted by the coefficients in a generating function could be mirrored by algebraic properties of the generating fu...We did quite a few examples that showed how combinatorial properties of arrangements counted by the coefficients in a generating function could be mirrored by algebraic properties of the generating functions themselves. The monomials x^i are called indicator polynomials. In general, a sequence of polynomials is called a family of indicator polynomials if there is one polynomial of each nonnegative integer degree in the sequence.
