Combinatorics

Graph

Mathematics

Mathematical analysis

Programming language

Path (computing)

Computer science

Expression (computer science)

Polynomial

Proyecciones (Antofagasta)

We determine a closed-form expression for the fifth characteristic coefficient of the power of a path. To arrive at this result, we establish the number of 4-cycles in the graph by means of their structural properties. The method developed might be applied to other well-structured graph classes in order to count 4-cycles or modified to count cycles of different length.

On the characteristic polynomial of the power of a path.