2015/06/02 by Johan Kok, Kok, Johan, Sudev Naduvath +4
Computer Science · Mathematics · #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems #math.CO #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.1506.00813
15 pages. The replacement now includes a title change and the section related to set-graphs. The paper has been submitted to the Taiwanese Journal of Mathematics for consideration
openalex publication_date 2015/06/02 · arxiv created 2015/06/04 · arxiv updated 2015/07/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we introduce the concept of curling subsequence of simple, finite and connected graphs. A curling subsequence is a maximal subsequence C of the degree sequence of a simple connected graph G for which the curling number cn(G) corresponds to the curling number of the degree sequence per se and hence we call it the curling number of the graph G. A maximal degree subsequence with equal entries is called an identity subsequence. The number of identity curling subsequences in a simple connected graph G is denoted ic(G). We show that the curling number conjecture holds for the degree sequence of a simple connected graph G on n ≥ 1 vertices. We also introduce the notion of the compound curling number of a simple connected graph G and then initiate a study on the curling number of certain standard graphs like Jaco graphs and set-graphs.