Unlocking the walk matrix of a graph

Fenjin Liu, Johannes Siemons

Let $G$ be a graph with vertex set $V=\{v_1,\dots ,v_n\}$ and adjacency matrix $A.$ For a subset $S$ of $V$ let $\e=(x_{1},\,\dots,\,x_{n})^{\tt T}$ be the characteristic vector…