Integer sequences with conjectured relation with certain graph parameters of the family of linear Jaco graphs

2025/07/22 by Johan Kok, Kok, Johan
Mathematics · #05B10 #05C07 #05C12 #05C30 #05C75 #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Graph theory and applications #Limits and Structures in Graph Theory

paper · pdf · doi:10.48550/arxiv.2507.16500

openalex publication_date 2025/07/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This experimental study presents some interesting conjectured relations between some integer sequences and certain graph parameters of the family of linear Jaco graphs J_n(x) where n = 1,2,3,…. It appears that Golden ratio-like floor function terms play an important role in the analysis of the graph structural properties of the family of linear Jaco graphs. The experimental methodology to obtain the conjectures is indeed trivial. However, it is the author's view that the proofs or disproofs of the conjectures may be challenging.

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