Tree-Line graphs and their quantum walks

Abstract

For a simple graph $\hat{I}“$, a (bipartite)tree-line graph and a tree-graph of $\hat{I}“$ can be defined. With a (bipartite)tree-line graph constructed by the function $(b)\ell$, we study the continuous quantum walk on $(b){\ell }^n\hat{I}“$. An equitable partition of a bipartite tree-line graph is obtained by its corresponding derived tree graph. This paper also examines quantum walks on derived graphs, whose vertices represent their basis state.

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