On extremal cacti with respect to the edge Szeged index and edge-vertex Szeged index

Abstract

The edge Szeged index and edge-vertex Szeged index of a graph are defined as Sz e (G) =respectively, where m u (uv|G) (resp., m v (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 n u (uv|G) (resp., n v (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.

Computation of edge Pi index, vertex Pi index and Szeged index of some cactus chains

“…The Szeged index was introduced by Gutman in 1994 in [18]. Since it has been found a great application in the modeling of physicochemical properties of chemical compounds, Szeged index has been studied by many researchers, see [19][20][21][22][23].…”

On cacti with large Mostar index

“…See [3,6,11,18,22] for various properties of the Szeged index of a graph. Some invariants such as edge Szeged index, revised Szeged index were also studied, see, e.g., [1,7,8,12,17,20,21]. Very recently, Doslić et al [4] introduced a new invariant -the Mostar index, of a connected graph G, defined as…”