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math.CO2013
On d-Walk Regular Graphs
Ernesto Estrada, Jose A. de la Pena
Let G be a graph with set of vertices 1,...,n and adjacency matrix A of size nxn. Let d(i,j)=d, we say that f_d:N->N is a d-function on G if for every pair of vertices i,j and k>=d…
math.CO2013
From Integer Sequences to Block Designs via Counting Walks in Graphs
Ernesto Estrada, José A. de la Peña
We define numbers of the type Oj(N) and Ej(N) and the corresponding integer sequences. We prove that these integer sequences, e.g., SO(N) and SE(N) correspond to the number of odd…