scholarly journals The Modified Wiener Index, Calculation of Harary Exponent and Multiplicative Wiener Index of Jahangir Graphs

2016 ◽  
Vol 06 (02) ◽  
pp. 46-50
Author(s):  
晶 张
Keyword(s):  
Wiener Index ◽  
Modified Wiener Index ◽  
Index Calculation

scholarly journals The modified Wiener index of some graph operations

2015 ◽  
Vol 11 (2) ◽  
pp. 277-284 ◽  
Author(s):  
Hossein Shabani ◽  
Ali Reza Ashrafi
Keyword(s):  
Wiener Index ◽  
Graph Operations ◽  
Modified Wiener Index

ON THE MODIFIED WIENER INDEX AND ITS CHEMICAL APPLICABILITY

2020 ◽  
Vol 9 (9) ◽  
pp. 7689-7698
Author(s):  
B. S. Durgi ◽  
S. M. Mekkalike ◽  
S. M. Hosamani
Keyword(s):  
Wiener Index ◽  
Modified Wiener Index

scholarly journals The Extremal Graphs of Some Topological Indices with Given Vertex k-Partiteness

Mathematics ◽  
2018 ◽  
Vol 6 (11) ◽  
pp. 271 ◽  
Author(s):  
Fang Gao ◽  
Xiaoxin Li ◽  
Kai Zhou ◽  
Jia-Bao Liu
Keyword(s):  
Wiener Index ◽  
Topological Indices ◽  
Extremal Graphs ◽  
Zeroth Order ◽  
First Zagreb Index ◽  
Zagreb Index ◽  
Randic Index ◽  
Laplacian Energy ◽  
Modified Wiener Index ◽  
Extremal Value

The vertex k-partiteness of graph G is defined as the fewest number of vertices whose deletion from G yields a k-partite graph. In this paper, we characterize the extremal value of the reformulated first Zagreb index, the multiplicative-sum Zagreb index, the general Laplacian-energy-like invariant, the general zeroth-order Randić index, and the modified-Wiener index among graphs of order n with vertex k-partiteness not more than m .

On Modified and Reverse Wiener Indices of Trees

2006 ◽  
Vol 61 (10-11) ◽  
pp. 536-540 ◽  
Author(s):  
Bing Zhang ◽  
Bo Zhou
Keyword(s):  
Wiener Index ◽  
Network Structures ◽  
Basic Requirement ◽  
Two Sides ◽  
Modified Wiener Index ◽  
Branching Index

The Wiener index is a well-known measure of graph or network structures with similarly useful variants of modified and reverse Wiener indices. The Wiener index of a tree T obeys the relation W(T)=nT,1(e)·nT,2(e) where nT,1(e) and nT,2(e) are the number of vertices of T lying on the two sides of the edge e, and where the summation goes over all edges of T. The λ -modified Wiener index is defined as mWλ (T) =[nT,1(e)·nT,2(e)]λ . For each λ > 0 and each integer d with 3 ≤ d ≤ n− 2, we determine the trees with minimal λ -modified Wiener indices in the class of trees with n vertices and diameter d. The reverse Wiener index of a tree T with n vertices is defined as Λ(T)=½n(n-1)d(T)-W(T), where d(T) is the diameter of T. We prove that the reverse Wiener index satisfies the basic requirement for being a branching index.

scholarly journals Distance-Based Polynomials and Topological Indices for Hierarchical Hypercube Networks

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Tingmei Gao ◽  
Iftikhar Ahmed
Keyword(s):  
Integral Equations ◽  
Chemical Compounds ◽  
Wiener Index ◽  
Topological Indices ◽  
Harary Index ◽  
Hypercube Networks ◽  
Modified Wiener Index

Topological indices are the numbers associated with the graphs of chemical compounds/networks that help us to understand their properties. The aim of this paper is to compute topological indices for the hierarchical hypercube networks. We computed Hosoya polynomials, Harary polynomials, Wiener index, modified Wiener index, hyper-Wiener index, Harary index, generalized Harary index, and multiplicative Wiener index for hierarchical hypercube networks. Our results can help to understand topology of hierarchical hypercube networks and are useful to enhance the ability of these networks. Our results can also be used to solve integral equations.

scholarly journals Partition and Colored Distances in Graphs Induced to Subsets of Vertices and Some of Its Applications

Symmetry ◽  
2020 ◽  
Vol 12 (12) ◽  
pp. 2027
Author(s):  
Mohammad Javad Nadjafi-Arani ◽  
Mahsa Mirzargar ◽  
Frank Emmert-Streib ◽  
Matthias Dehmer
Keyword(s):  
Transitive Closure ◽  
Weighted Graph ◽  
Wiener Index ◽  
Upper Bounds ◽  
Two Dimensional ◽  
Graph Invariants ◽  
Partition Distance ◽  
Cut Method ◽  
Partial Cube ◽  
Modified Wiener Index

If G is a graph and P is a partition of V(G), then the partition distance of G is the sum of the distances between all pairs of vertices that lie in the same part of P. A colored distance is the dual concept of the partition distance. These notions are motivated by a problem in the facility location network and applied to several well-known distance-based graph invariants. In this paper, we apply an extended cut method to induce the partition and color distances to some subsets of vertices which are not necessary a partition of V(G). Then, we define a two-dimensional weighted graph and an operator to prove that the induced partition and colored distances of a graph can be obtained from the weighted Wiener index of a two-dimensional weighted quotient graph induced by the transitive closure of the Djoković–Winkler relation as well as by any partition that is coarser. Finally, we utilize our main results to find some upper bounds for the modified Wiener index and the number of orbits of partial cube graphs under the action of automorphism group of graphs.

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
Sign in / Sign up

Export Citation Format

Share Document