2018/04/17 by Shengjie He, Rong‐Xia Hao, He, Shengjie +3
Mathematics · #Analytic and geometric function theory #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications #Mathematical Approximation and Integration
paper · pdf · doi:10.48550/arxiv.1804.06009
openalex publication_date 2018/04/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let G be a connected graph. The edge revised Szeged index of G is defined as Sz∗e(G)=∑e=uv∈ E(G)(mu(e|G)+\fracm0(e|G)2)(mv(e|G)+\fracm0(e|G)2), where mu(e|G) (resp., mv(e|G)) is the number of edges whose distance to vertex u (resp., v) is smaller than the distance to vertex v (resp., u), and m0(e|G) is the number of edges equidistant from both ends of e. In this paper, we give the minimal and the second minimal edge revised Szeged index of cacti with order n and k cycles, and all the graphs that achieve the minimal and second minimal edge revised Szeged index are identified.