2022/11/05 by Peichao Wei, Wei, Peichao, Muhuo Liu +1 · 2 citations
Chemistry · Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications #Metal-Organic Frameworks: Synthesis and Applications #Synthesis and Properties of Aromatic Compounds
paper · pdf · doi:10.48550/arxiv.2211.02911
openalex publication_date 2022/11/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For a simple connected graph G=(V,E), let d(u) be the degree of the vertex u of G. The general Sombor index of G is defined as SOα(G)=∑uv∈ E [d(u)2+d(v)2]α where SO(G)=SO0.5(G) is the recently invented Sombor index. In this paper, we show that in the class of connected graphs with a fixed degree sequence (for which the minimum degree being equal to one), there exists a special extremal BFS-graph with minimum general Sombor index for 0<α<1 (resp. maximum general Sombor index for either α>1 or α<0). Moreover, for any given tree, unicyclic, and bicyclic degree sequences with minimum degree 1, there exists a unique extremal BFS-graph with minimum general Sombor index for 0<α<1 and maximum general Sombor index for either α>1 or α<0.