Abstract
The P edge Szeged index and edge-vertex Szeged index of a graph are defined as Sze(G) = uv?E(G) mu(uvjG)mv(uvjG) and Szev(G) = 1 2 P uv?E(G) [nu(uvjG)mv(uvjG) + nv(uvjG)mu(uvjG)]; respectively, where mu(uvjG) (resp., mv(uvjG)) and nu(uvjG) (resp., nv(uvjG)) are the number of edges and 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.
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