Orientations of hexagonal chains with extremal values of the Randić index

2021 ◽  
Author(s):  
Sergio Bermudo ◽  
Juan Monsalve ◽  
Juan Rada
Keyword(s):  
Randić Index ◽  
Randic Index ◽  
Extremal Values

A short note on tetracyclic graphs with extremal values of Randić index

2019 ◽  
Vol 13 (06) ◽  
pp. 2050105 ◽  
Author(s):  
Suresh Elumalai ◽  
Toufik Mansour
Keyword(s):  
Short Note ◽  
Simple Graph ◽  
Vertex Degree ◽  
Randić Index ◽  
Correct Version ◽  
Randic Index ◽  
Extremal Values

Let [Formula: see text] be a simple graph. The Randić index of [Formula: see text] is defined as the sum of [Formula: see text] over all edges [Formula: see text] of [Formula: see text], where [Formula: see text] denotes the vertex degree of [Formula: see text] in [Formula: see text]. Dehghan-Zadeh, Ashrafi and Habibi gave Tetracyclic graphs with extremal values of Randić index. We first point out that Theorem 1 is not completely correct and the number of nonisomorphic tetracyclic graphs on seven vertices given in Fig. 4 is incomplete and incorrect and in this short note, we present the correct version of it.

scholarly journals Extremal Values of Randić Index among Some Classes of Graphs

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Ali Ghalavand ◽  
Ali Reza Ashrafi ◽  
Marzieh Pourbabaee
Keyword(s):  
Upper Bounds ◽  
Simple Graph ◽  
Randić Index ◽  
Lower And Upper Bounds ◽  
Randic Index ◽  
Chemical Graphs ◽  
Cyclic Graphs ◽  
Vertex Degrees ◽  
Extremal Values

Suppose G is a simple graph with edge set E G . The Randić index R G is defined as R G = ∑ u v ∈ E G 1 / deg G u deg G v , where deg G u and deg G v denote the vertex degrees of u and v in G , respectively. In this paper, the first and second maximum of Randić index among all n − vertex c − cyclic graphs was computed. As a consequence, it is proved that the Randić index attains its maximum and second maximum on two classes of chemical graphs. Finally, we will present new lower and upper bounds for the Randić index of connected chemical graphs.

Tetracyclic graphs with extremal values of Randić index

2015 ◽  
Vol 8 (1) ◽  
pp. 9-16 ◽  
Author(s):  
T. Dehghan-Zadeh ◽  
A. R. Ashrafi ◽  
N. Habibi
Keyword(s):  
Randić Index ◽  
Randic Index ◽  
Extremal Values

Extremal values for the variation of the Randić index of bicyclic graphs

2021 ◽  
Vol 51 (4) ◽  
Author(s):  
Jian-Bo Lv ◽  
Jianxi Li
Keyword(s):  
Randić Index ◽  
Randic Index ◽  
Bicyclic Graphs ◽  
Extremal Values

Maximally edge-connected graphs and Zeroth-order general Randić index for $$\alpha \le -1$$ α ≤ - 1

2014 ◽  
Vol 31 (1) ◽  
pp. 182-195 ◽  
Author(s):  
Guifu Su ◽  
Liming Xiong ◽  
Xiaofeng Su ◽  
Guojun Li
Keyword(s):  
Randić Index ◽  
Zeroth Order ◽  
Connected Graphs ◽  
Randic Index ◽  
General Randić Index ◽  
General Randic Index

Second order Randić index of phenylenes and their corresponding hexagonal squeezes

2006 ◽  
Vol 42 (4) ◽  
pp. 941-947 ◽  
Author(s):  
Jie Zhang ◽  
Hanyuan Deng ◽  
Shubo Chen
Keyword(s):  
Second Order ◽  
Randić Index ◽  
Randic Index

scholarly journals Ordering of alkane isomers by means of connectivity indices

2002 ◽  
Vol 67 (2) ◽  
pp. 87-97 ◽  
Author(s):  
Ivan Gutman ◽  
Dusica Vidovic ◽  
Anka Nedic
Keyword(s):  
Carbon Atom ◽  
Organic Molecule ◽  
Molecular Graph ◽  
Connectivity Index ◽  
Randić Index ◽  
Randic Index ◽  
Connectivity Indices ◽  
The Difference

The connectivity index of an organic molecule whose molecular graph is Gis defined as C(?)=?(?u?v)??where ?u is the degree of the vertex u in G, where the summation goes over all pairs of adjacent vertices of G and where ? is a pertinently chosen exponent. The usual value of ? is ?1/2, in which case ?=C(?1/2) is referred to as the Randic index. The ordering of isomeric alkanes according to ??follows the extent of branching of the carbon-atom skeleton. We now study the ordering of the constitutional isomers of alkanes with 6 through 10 carbon atoms with respect to C(?) for various values of the parameter ?. This ordering significantly depends on ?. The difference between the orderings with respect to ??and with respect to C(?) is measured by a function ??and the ?-dependence of ??was established.

The exponent in the general Randić index

2006 ◽  
Vol 43 (1) ◽  
pp. 32-44 ◽  
Author(s):  
Lane Clark ◽  
Ivan Gutman
Keyword(s):  
Randić Index ◽  
Randic Index ◽  
General Randić Index ◽  
General Randic Index

scholarly journals On the conjecture of Aouchiche and Hansen about the Randić index

2013 ◽  
Vol 313 (3) ◽  
pp. 225-235 ◽  
Author(s):  
Bolian Liu ◽  
Ljiljana R. Pavlović ◽  
Tomica R. Divnić ◽  
Jianxi Liu ◽  
Marina M. Stojanović
Keyword(s):  
Randić Index ◽  
Randic Index

scholarly journals Bounds on General Randić Index for F-Sum Graphs

2020 ◽  
Vol 2020 ◽  
pp. 1-17
Author(s):  
Xu Li ◽  
Maqsood Ahmad ◽  
Muhammad Javaid ◽  
Muhammad Saeed ◽  
Jia-Bao Liu
Keyword(s):  
Molecular Graph ◽  
Randić Index ◽  
Lower And Upper Bounds ◽  
First Zagreb Index ◽  
Zagreb Index ◽  
Randic Index ◽  
Structure Activity ◽  
General Randić Index ◽  
General Randic Index ◽  
The First Zagreb Index

A topological invariant is a numerical parameter associated with molecular graph and plays an imperative role in the study and analysis of quantitative structure activity/property relationships (QSAR/QSPR). The correlation between the entire π-electron energy and the structure of a molecular graph was explored and understood by the first Zagreb index. Recently, Liu et al. (2019) calculated the first general Zagreb index of the F-sum graphs. In the same paper, they also proposed the open problem to compute the general Randić index RαΓ=∑uv∈EΓdΓu×dΓvα of the F-sum graphs, where α∈R and dΓu denote the valency of the vertex u in the molecular graph Γ. Aim of this paper is to compute the lower and upper bounds of the general Randić index for the F-sum graphs when α∈N. We present numerous examples to support and check the reliability as well as validity of our bounds. Furthermore, the results acquired are the generalization of the results offered by Deng et al. (2016), who studied the general Randić index for exactly α=1.

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