Results 11 to 20 of about 894 (87)
On minimum revised edge Szeged index of bicyclic graphs
AKCE International Journal of Graphs and Combinatorics, 2022 The revised edge Szeged index [Formula: see text] of a graph G is defined as [Formula: see text] where [Formula: see text] and [Formula: see text] are, respectively, the number of edges of G lying closer to vertex u than to vertex v and the number of ...
Mengmeng Liu, Shengjin Ji
doaj +4 more sources
The quotients between the (revised) Szeged index and Wiener index of graphs [PDF]
Discrete Mathematics & Theoretical Computer Science, 2017 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 $n\geqslant 10$ are ...
Huihui Zhang, Jing Chen, Shuchao Li
doaj +4 more sources
Revised Szeged Index and Revised Edge Szeged Index of Certain Special Molecular Graphs [PDF]
International Journal of Applied Physics and Mathematics, 2014 In theoretical chemistry, the revised Szeged index and revised Szeged edge index were introduced to measure the stability of alkanes and the strain energy of cycloalkanes. In this paper, by virtue of mathematical derivation, we determine the revised Szeged index and revised edge Szeged index of fan molecular graph, wheel molecular graph, gear fan ...
Yun Gao, Wei Gao, Li Liang
openaire +1 more source
Comparing Wiener, Szeged and revised Szeged index on cactus graphs
Ars Mathematica Contemporanea, 2023 12 pages, 3 ...
openaire +2 more sources
The (revised) Szeged index and the Wiener index of a nonbipartite graph
European Journal of Combinatorics, 2014 Hansen et. al. used the computer programm AutoGraphiX to study the differences between the Szeged index $Sz(G)$ and the Wiener index $W(G)$, and between the revised Szeged index $Sz^*(G)$ and the Wiener index for a connected graph $G$. They conjectured that for a connected nonbipartite graph $G$ with $n \geq 5$ vertices and girth $g \geq 5,$ $ Sz(G)-W ...
Lily Chen +2 more
openaire +2 more sources
Topological edge properties of C60+12n fullerenes
Beilstein Journal of Nanotechnology, 2013 A molecular graph M is a simple graph in which atoms and chemical bonds are the vertices and edges of M, respectively. The molecular graph M is called a fullerene graph, if M is the molecular graph of a fullerene molecule.
A. Mottaghi, Ali R. Ashrafi
doaj +1 more source
The extremal unicyclic graphs with given diameter and minimum edge revised Szeged index
AIMS Mathematics, 2023 <abstract><p>Let $ H $ be a connected graph. The edge revised Szeged index of $ H $ is defined as $ Sz^{\ast}_{e}(H) = \sum\limits_{e = uv\in E_H}(m_{u}(e|H)+\frac{m_{0}(e|H)}{2})(m_{v}(e|H)+\frac{m_{0}(e|H)}{2}) $, where $ m_{u}(e|H) $ (resp., $ m_{v}(e|H) $) is the number of edges whose distance to vertex $ u $ (resp., $ v $) is smaller ...
Shengjie He, Qiaozhi Geng, Rong-Xia Hao
openaire +2 more sources
Studying the corona product of graphs under some graph invariants [PDF]
Transactions on Combinatorics, 2014 The corona product $Gcirc H$ of two graphs $G$ and $H$ is obtained by taking one copy of $G$ and $|V(G)|$ copies of $H$; and by joining each vertex of the $i$-th copy of $H$ to the $i$-th vertex of $G$, where $1 leq i leq |V(G)|$.
M. Tavakoli +2 more
doaj
The extremal unicyclic graphs of the revised edge Szeged index with given diameter
, 2023 Let $G$ be a connected graph. The revised edge Szeged index of $G$ is defined as $Sz^{\ast}_{e}(G)=\sum\limits_{e=uv\in E(G)}(m_{u}(e|G)+\frac{m_{0}(e|G)}{2})(m_{v}(e|G)+\frac{m_{0}(e|G)}{2})$, 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., $u$)
He, Shengjie +2 more
openaire +2 more sources
Steiner (revised) Szeged index of graphs
, 2019 12 ...
Ghorbani, Modjtaba +5 more
openaire +3 more sources