2011/03/10 by Marcin Anholcer, Michał Karoński, Anholcer, Marcin +4
Computer Science · Mathematics · #(05C15) #05C78 #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems #Limits and Structures in Graph Theory #math.CO #msc:05C78
paper · pdf · doi:10.48550/arxiv.1103.2087
The stronger results for trees were recently proved by Nurdin et al. (Nurdin, Baskoro E.T., Salman A.N.M., Gaos N.N., On the Total Vertex Irregularity Strength of Trees, Discrete Mathematics 310 (2010), 3043-3048.). However we decided to publish our paper for two reasons. Firstly, we consider more general case of forests, not only trees. Secondly, we use different proof technique
arxiv created 2011/03/10 · openalex publication_date 2011/03/10 · arxiv updated 2011/03/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We investigate a graph parameter called the total vertex irregularity strength (tvs(G)), i.e. the minimal s such that there is a labeling w: E(G)∪ V(G)→ \1,2,..,s\ of the edges and vertices of G giving distinct weighted degrees wtG(v):=w(v)+∑v∈ e ∈ E(G)w(e) for every pair of vertices of G. We prove that tvs(F)=\lceil (n1+1)/2 \rceil for every forest F with no vertices of degree 2 and no isolated vertices, where n1 is the number of pendant vertices in F. Stronger results for trees were recently proved by Nurdin et al.