ﻻ يوجد ملخص باللغة العربية
Let $G$ be a connected graph. The edge revised Szeged index of $G$ is defined as $Sz^{ast}_{e}(G)=sumlimits_{e=uvin E(G)}(m_{u}(e|G)+frac{m_{0}(e|G)}{2})(m_{v}(e|G)+frac{m_{0}(e|G)}{2})$, where $m_{u}(e|G)$ (resp., $m_{v}(e|G)$) is the number of edges whose distance to vertex $u$ (resp., $v$) is smaller than the distance to vertex $v$ (resp., $u$), and $m_{0}(e|G)$ 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.
The edge Szeged index and edge-vertex Szeged index of a graph are defined as $Sz_{e}(G)=sumlimits_{uvin E(G)}m_{u}(uv|G)m_{v}(uv|G)$ and $Sz_{ev}(G)=frac{1}{2} sumlimits_{uv in E(G)}[n_{u}(uv|G)m_{v}(uv|G)+n_{v}(uv|G)m_{u}(uv|G)],$ respectively, wher
An extension of the well-known Szeged index was introduced recently, named as weighted Szeged index ($textrm{sz}(G)$). This paper is devoted to characterizing the extremal trees and graphs of this new topological invariant. In particular, we proved t
The edge Szeged index of a graph $G$ is defined as $Sz_{e}(G)=sumlimits_{uvin E(G)}m_{u}(uv|G)m_{v}(uv|G)$, 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 ve
Let $Sz(G),Sz^*(G)$ and $W(G)$ be the Szeged index, revised Szeged index and Wiener index of a graph $G.$ In this paper, the graphs with the fourth, fifth, sixth and seventh largest Wiener indices among all unicyclic graphs of order $ngeqslant 10$ ar
The edge-Wiener index $W_e(G)$ of a connected graph $G$ is the sum of distances between all pairs of edges of $G$. A connected graph $G$ is said to be a cactus if each of its blocks is either a cycle or an edge. Let $mathcal{G}_{n,t}$ denote the clas