2017/11/07 by Shengjie He, Rong‐Xia Hao, He, Shengjie +3 · 1 citation
Computer Science · Engineering · Mathematics · #Advanced Graph Theory Research #Catalysis for Biomass Conversion #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications
paper · pdf · doi:10.48550/arxiv.1711.02394
openalex publication_date 2017/11/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The edge Szeged index and edge-vertex Szeged index of a graph are defined as Sze(G)=∑uv∈ E(G)mu(uv|G)mv(uv|G) and Szev(G)=(1)/(2) ∑uv ∈ E(G)[nu(uv|G)mv(uv|G)+nv(uv|G)mu(uv|G)], respectively, where mu(uv|G) (resp., mv(uv|G)) is the number of edges whose distance to vertex u (resp., v) is smaller than the distance to vertex v (resp., u), and nu(uv|G) (resp., nv(uv|G)) is the number of vertices whose distance to vertex u (resp., v) is smaller than the distance to vertex v (resp., u), respectively. A cactus is a graph in which any two cycles have at most one common vertex. In this paper, the lower bounds of edge Szeged index and edge-vertex Szeged index for cacti with order n and k cycles are determined, and all the graphs that achieve the lower bounds are identified.