2018/08/19 by Richard J. Mathar, Mathar, Richard J.
Computer Science · Mathematics · #05C30 #05C38 (Primary) 05A15 (Secondary) #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph Theory and Algorithms #Graph theory and applications
paper · pdf · doi:10.48550/arxiv.1808.06264
openalex publication_date 2018/08/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The simple connected graphs may be classified by their cycle composition (number and lengths of cycles). This work derives the counting series of the simple connected graphs that have cycles of unrestricted number and length, but no overlapping cycles. Cycle pairs of these graphs of interest must not have common nodes or edges. The recipe of counting these graphs is based on the counting series of the associated planted graphs, multisets of planted graphs, a recursive synthesis of enriched trees, and a generalized Otter's formula that maps the underlying rooted block graphs to the underlying block graphs.