On algorithms for enumerating BC-subtrees of unicyclic and edge-disjoint bicyclic graphs

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• 作者：Yu Yang^a ; ^b ; ^{yangyugdzs@gmail.com" class="auth_mail" title="E-mail the corresponding author} ; Hongbo Liu^a ; ^c ; ^{hongbo@sccn.ucsd.edu" class="auth_mail" title="E-mail the corresponding author} ; Hua Wang^b ; ^{hwang@georgiasouthern.edu" class="auth_mail" title="E-mail the corresponding author} ; Shigang Feng^a ; ^{shgfeng@dlmu.edu.cn" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Block-cutpoint-tree ; BC-subtrees ; Unicyclic graphs ; Edge-disjoint bicyclic graphs ; Generating function ; Enumeration
• 刊名：Discrete Applied Mathematics
• 出版年：2016
• 出版时间：20 April 2016
• 年：2016
• 卷：203
• 期：Complete
• 页码：184-203
• 全文大小：527 K

文摘

A BC-tree (block-cutpoint-tree) is a tree (with at least two vertices) where the distance between any two leaves is even. A BC-subtree is a subtree of a connected graph that is also a BC-tree. In this paper, we first consider subtrees containing a specific vertex with conditions on the parity of the distances from this vertex to the leaves and the enumeration of such subtrees of unicyclic and edge-disjoint bicyclic graphs. Using these results and through generating functions of BC-subtrees, we present graph-theoretical based algorithms for enumerating BC-subtrees, BC-subtrees containing a given vertex, and BC-subtrees containing two distinct vertices of unicyclic and edge-disjoint bicyclic graphs. These results also provide a novel perspective on exploring the structural properties of molecules.