2024/01/14 by Yunfang Tang, Tang, Yunfang, Yuting Yao +1
Chemistry · Computer Science · Medicine · #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems #Multicomponent Synthesis of Heterocycles #Synthesis of Organic Compounds
paper · pdf · doi:10.48550/arxiv.2401.07254
openalex publication_date 2024/01/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A total weighting of a graph G is a mapping ϕ that assigns a weight to each vertex and each edge of G. The vertex-sum of v ∈ V(G) with respect to ϕ is Sϕ(v)=∑e∈ E(v)ϕ(e)+ϕ(v). A total weighting is proper if adjacent vertices have distinct vertex-sums. A graph G=(V,E) is called (k,k')-choosable if the following is true: If each vertex x is assigned a set L(x) of k real numbers, and each edge e is assigned a set L(e) of k' real numbers, then there is a proper total weighting ϕ with ϕ(y)∈ L(y) for any y ∈ V ∪ E. In this paper, we prove that the generalized Petersen graphs are (1,3)-choosable.