ABSTRACT
The walk generating function Wij (G, x) counts the walks in the graph G which start at the vertex i and finish on the vertex j. In Section 1 of this chapter we use a determinental identity due to Jacobi to prove that x − 1 W i j ( G , x − 1 ) = ( ϕ ( G \ i , x ) ϕ ( G \ j , x ) − ϕ ( G , x ) ϕ ( G \ i j , x ) 1 / 2 ϕ ( G , x ) . https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315137131/3e789cab-79f2-434a-a841-e2acf5146c2d/content/eq299.tif"/>
