The Harary Index of Trees with At Most One Generalized Center Vertex

2017 ◽  
Author(s):  
Shengzhang Ren ◽  
Fang-an Deng
Keyword(s):  
Harary Index ◽  
Generalized Center

Harary index of Eulerian graphs

2021 ◽  
Author(s):  
Junqing Cai ◽  
Panpan Wang ◽  
Linlin Zhang
Keyword(s):  
Harary Index ◽  
Eulerian Graphs

The Harary index of ordinary and generalized quasi-tree graphs

2013 ◽  
Vol 45 (1-2) ◽  
pp. 365-374 ◽  
Author(s):  
Kexiang Xu ◽  
Jinlan Wang ◽  
Hongshuang Liu
Keyword(s):  
Harary Index ◽  
Tree Graphs

Minimal Harary index of unicyclic graphs with diameter at most 4

2020 ◽  
Vol 381 ◽  
pp. 125315
Author(s):  
Lihua Feng ◽  
Ziyuan Li ◽  
Weijun Liu ◽  
Lu Lu ◽  
Dragan Stevanović
Keyword(s):  
Harary Index ◽  
Unicyclic Graphs

scholarly journals Hosoya and Harary Polynomials of TOX(n),RTOX(n),TSL(n) and RTSL(n)

2019 ◽  
Vol 2019 ◽  
pp. 1-18 ◽  
Author(s):  
Lian Chen ◽  
Abid Mehboob ◽  
Haseeb Ahmad ◽  
Waqas Nazeer ◽  
Muhammad Hussain ◽  
...  
Keyword(s):  
Topological Index ◽  
Molecular Descriptor ◽  
Wiener Index ◽  
Vital Role ◽  
Harary Index ◽  
Chemical Graph ◽  
Chemical Graph Theory ◽  
Hosoya Polynomial ◽  
Molecular Branching ◽  
Path Number

In the fields of chemical graph theory, topological index is a type of a molecular descriptor that is calculated based on the graph of a chemical compound. In 1947, Wiener introduced “path number” which is now known as Wiener index and is the oldest topological index related to molecular branching. Hosoya polynomial plays a vital role in determining Wiener index. In this report, we computed the Hosoya and the Harary polynomials for TOX(n),RTOX(n),TSL(n), and RTSL(n) networks. Moreover, we computed serval distance based topological indices, for example, Wiener index, Harary index, and multiplicative version of wiener index.

scholarly journals Extremal Bipartite Graphs with Given Parameters on the Resistance–Harary Index

Symmetry ◽  
2019 ◽  
Vol 11 (5) ◽  
pp. 615
Author(s):  
Hongzhuan Wang ◽  
Piaoyang Yin
Keyword(s):  
Lower Bound ◽  
Bipartite Graph ◽  
Extremal Graphs ◽  
Graph Invariant ◽  
Resistance Distance ◽  
Harary Index ◽  
H Index ◽  
Electronic Networks ◽  
Minimum Number ◽  
Graph Parameters

Resistance distance is a concept developed from electronic networks. The calculation of resistance distance in various circuits has attracted the attention of many engineers. This report considers the resistance-based graph invariant, the Resistance–Harary index, which represents the sum of the reciprocal resistances of any vertex pair in the figure G, denoted by R H ( G ) . Vertex bipartiteness in a graph G is the minimum number of vertices removed that makes the graph G become a bipartite graph. In this study, we give the upper bound and lower bound of the R H index, and describe the corresponding extremal graphs in the bipartite graph of a given order. We also describe the graphs with maximum R H index in terms of graph parameters such as vertex bipartiteness, cut edges, and matching numbers.

scholarly journals Harary index of the k-th power of a graph

2013 ◽  
Vol 7 (1) ◽  
pp. 94-105 ◽  
Author(s):  
Guifu Su ◽  
Liming Xiong ◽  
Ivan Gutman
Keyword(s):  
Type Inequality ◽  
Upper Bounds ◽  
Lower And Upper Bounds ◽  
Harary Index ◽  
Underlying Graph

The k-th power of a graph G, denoted by Gk, is a graph with the same set of vertices as G, such that two vertices are adjacent in Gk if and only if their distance in G is at most k. The Harary index H is the sum of the reciprocal distances of all pairs of vertices of the underlying graph. Lower and upper bounds on H(Gk) are obtained. A Nordhaus-Gaddum type inequality for H(Gk) is also established.

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