Abstract
A multiple leaf-distance granular regular α-tree (abbreviated as LDR α-tree for short) is a tree (with at least α+1 vertices) where any two leaves are at some distance divisible by α. A connected graph's subtree which is additionally an LDR α-tree is known as an LDR α-subtree. Obviously, α=1 and 2, correspond to the general subtrees (excluding the single vertex subtrees) and the BC-subtrees (the distance between any two leaves of the subtree is even), respectively. With generating functions and structure decomposition, in this paper, we propose algorithms for enumerating an auxiliary subtree ατ(v)-subtree (τ=0,1,…,α−1) containing a fixed vertex, and various LDR α-subtrees of unicyclic graphs, respectively. Basing on these algorithms, we further present algorithms for enumerating various LDR α-subtrees of edge-disjoint bicyclic graphs.
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