Remarks on the Wiener index of unicyclic graphs

2012 ◽  
Vol 41 (1-2) ◽  
pp. 49-59 ◽  
Author(s):  
R. Nasiri ◽  
H. Yousefi-Azari ◽  
M. R. Darafsheh ◽  
A. R. Ashrafi
Keyword(s):  
Wiener Index ◽  
Unicyclic Graphs

scholarly journals Unicyclic Graphs with the Fourth Extremal Wiener Indices

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Guangfu Wang ◽  
Yujun Yang ◽  
Yuliang Cao ◽  
Shoujun Xu
Keyword(s):  
Wiener Index ◽  
Unicyclic Graphs

A graph is called unicyclic if the graph contains exactly one cycle. Unicyclic graphs with the fourth extremal Wiener indices are characterized. It is shown that, among all unicyclic graphs with n≥8 vertices, C5Sn−4 and C2u1,u2S3,Sn−4 attain the fourth minimum Wiener index, whereas C3u1,u2P3,Pn−4 attains the fourth maximum Wiener index.

The Wiener index of unicyclic graphs given number of pendant vertices or cut vertices

2016 ◽  
Vol 55 (1-2) ◽  
pp. 1-24 ◽  
Author(s):  
Shang-wang Tan ◽  
Qi-long Wang ◽  
Yan Lin
Keyword(s):  
Wiener Index ◽  
Unicyclic Graphs

scholarly journals Algorithms for Computing Wiener Indices of Acyclic and Unicyclic Graphs

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-6
Author(s):  
Bo Bi ◽  
Muhammad Kamran Jamil ◽  
Khawaja Muhammad Fahd ◽  
Tian-Le Sun ◽  
Imran Ahmad ◽  
...  
Keyword(s):  
Physical Properties ◽  
Topological Index ◽  
Linear Time ◽  
Molecular Graph ◽  
Wiener Index ◽  
Time Algorithm ◽  
Linear Time Algorithm ◽  
Unicyclic Graphs ◽  
Polarity Index ◽  
Acyclic Graphs

Let G = V G , E G be a molecular graph, where V G and E G are the sets of vertices (atoms) and edges (bonds). A topological index of a molecular graph is a numerical quantity which helps to predict the chemical/physical properties of the molecules. The Wiener, Wiener polarity, and the terminal Wiener indices are the distance-based topological indices. In this paper, we described a linear time algorithm (LTA) that computes the Wiener index for acyclic graphs and extended this algorithm for unicyclic graphs. The same algorithms are modified to compute the terminal Wiener index and the Wiener polarity index. All these algorithms compute the indices in time O n .

scholarly journals The reciprocal reverse Wiener index of unicyclic graphs

Filomat ◽  
2014 ◽  
Vol 28 (2) ◽  
pp. 249-255
Author(s):  
Jianping Li ◽  
Bo Zhou
Keyword(s):  
Connected Graph ◽  
Wiener Index ◽  
Extremal Graphs ◽  
Unicyclic Graphs ◽  
Mathematical Chemistry

The reciprocal reverse Wiener index R?(G) of a connected graph G is defined in mathematical chemistry as the sum of weights 1/d(G)?dG(u,v) of all unordered pairs of distinct vertices u and v with dG(u, v) < d(G), where dG(u, v) is the distance between vertices u and v in G and d(G) is the diameter of G. We determine the minimum and maximum reciprocal reverse Wiener indices in the class of n-vertex unicyclic graphs and characterize the corresponding extremal graphs.

scholarly journals Wiener index of unicycle graphs with given number of even degree vertices

2020 ◽  
Vol 12 (04) ◽  
pp. 2050054
Author(s):  
Peter Luo ◽  
Cun-Quan Zhang ◽  
Xiao-Dong Zhang
Keyword(s):  
Experimental Data ◽  
Connected Graph ◽  
Wiener Index ◽  
Structural Result ◽  
Unicyclic Graphs

The Wiener index of a connected graph is the sum of the distance of all pairs of distinct vertices. It was introduced by Wiener in 1947 to analyze some aspects of branching by fitting experimental data for several properties of alkane compounds. Denote by [Formula: see text] the set of unicyclic graphs with [Formula: see text] vertices and [Formula: see text] vertices of even degree. In this paper, we present a structural result on the graphs in [Formula: see text] with minimum Wiener index and completely characterize such graphs when [Formula: see text].

Allelopathic and Medicinal plant. 26. Millettia speciosa

2020 ◽  
Vol 51 (2) ◽  
pp. 125-146
Author(s):  
Nasiruddin Nasiruddin ◽  
Yu Zhangxin ◽  
Ting Zhao Chen Guangying ◽  
Minghui Ji
Keyword(s):  
Community Structure ◽  
Medicinal Plant ◽  
Gel Electrophoresis ◽  
Denaturing Gradient Gel Electrophoresis ◽  
Wiener Index ◽  
Pseudomonas Spp ◽  
Evenness Index ◽  
Gradient Gel Electrophoresis ◽  
Rhizosphere Pseudomonas

We grew cucumber in pots in greenhouse for 9-successive cropping cycles and analyzed the rhizosphere Pseudomonas spp. community structure and abundance by PCR-denaturing gradient gel electrophoresis and quantitative PCR. Results showed that continuous monocropping changed the cucumber rhizosphere Pseudomonas spp. community. The number of DGGE bands, Shannon-Wiener index and Evenness index decreased during the 3rd cropping and thereafter, increased up to the 7th cropping, however, however, afterwards they decreased again. The abundance of Pseudomonas spp. increased up to the 5th successive cropping and then decreased gradually. These findings indicated that the structure and abundance of Pseudomonas spp. community changed with long-term cucumber monocropping, which might be linked to soil sickness caused by its continuous monocropping.

T Wiener Index of Fibonacci Labeled Graph Pn ʘ F4

2018 ◽  
Vol 9 (11) ◽  
pp. 1712-1716
Author(s):  
R. Palanikumar ◽  
A. Rameshkumar
Keyword(s):  
Wiener Index ◽  
Labeled Graph
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