Geodesic
The path polynomial of a complete graph
The electronic journal of linear algebra, Tome 10 (2003), pp. 155-162.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: Let $Pk(x)$ denote the polynomial of the path on k vertices. A complete description of the matrix that is the obtained by evaluating $Pk(x)$ at the adjacency matrix of the complete graph, along with computing the effect of evaluating $Pk(x)$ with Laplacian matrices of a path and of a circuit.
Classification : 05C38, 05C50
Keywords: graph, adjacency matrix, Laplacian matrix, characteristic polynomial 
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da Fonseca, C. M. The path polynomial of a complete graph. The electronic journal of linear algebra, Tome 10 (2003), pp. 155-162. http://geodesic.mathdoc.fr/item/ELA_2003__10__a13/