Path polynomials of a circuit: a constructive approach
Carlos M. da Fonseca, J. Petronilho · Linear and Multilinear Algebra · 1998
Let Pk denote the polynomial of the path on k vertices. We describe completely the matrix Pk (Cn ), where Cn is the circuit on n vertices, using some important concepts of theory of circulant matrices. We also consider Q k , the polynomial of the circuit on kvertices. Using orthogonal polynomials we present constructive proofs of some results obtained recently by Bapat and Lai, Beezer and Ronghua.