Comparison between the zeroth-order Randić index and the sum-connectivity index

2016 ◽  
Vol 274 ◽  
pp. 585-589 ◽  
Author(s):  
Kinkar Ch. Das ◽  
Matthias Dehmer
Keyword(s):  
Connectivity Index ◽  
Randić Index ◽  
Zeroth Order ◽  
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.

scholarly journals First General Zagreb Index of Generalized F-sum Graphs

2020 ◽  
Vol 2020 ◽  
pp. 1-16 ◽  
Author(s):  
H. M. Awais ◽  
Muhammad Javaid ◽  
Akbar Ali
Keyword(s):  
Real Number ◽  
Cartesian Product ◽  
Randić Index ◽  
Zeroth Order ◽  
Zagreb Index ◽  
Randic Index

The first general Zagreb (FGZ) index (also known as the general zeroth-order Randić index) of a graph G can be defined as M γ G = ∑ u v ∈ E G d G γ − 1 u + d G γ − 1 v , where γ is a real number. As M γ G is equal to the order and size of G when γ = 0 and γ = 1 , respectively, γ is usually assumed to be different from 0 to 1. In this paper, for every integer γ ≥ 2 , the FGZ index M γ is computed for the generalized F-sums graphs which are obtained by applying the different operations of subdivision and Cartesian product. The obtained results can be considered as the generalizations of the results appeared in (IEEE Access; 7 (2019) 47494–47502) and (IEEE Access 7 (2019) 105479–105488).

scholarly journals Connected (n,m)-graphs with minimum and maximum zeroth-order general Randić index

2007 ◽  
Vol 155 (8) ◽  
pp. 1044-1054 ◽  
Author(s):  
Yumei Hu ◽  
Xueliang Li ◽  
Yongtang Shi ◽  
Tianyi Xu
Keyword(s):  
Randić Index ◽  
Zeroth Order ◽  
Randic Index ◽  
General Randić Index ◽  
General Randic Index

scholarly journals Some Bounds on Zeroth-Order General Randić Index

Mathematics ◽  
2020 ◽  
Vol 8 (1) ◽  
pp. 98 ◽  
Author(s):  
Muhammad Kamran Jamil ◽  
Ioan Tomescu ◽  
Muhammad Imran ◽  
Aisha Javed
Keyword(s):  
Clique Number ◽  
Upper Bounds ◽  
Randić Index ◽  
Extremal Graphs ◽  
Lower And Upper Bounds ◽  
Zeroth Order ◽  
Randic Index ◽  
General Randić Index ◽  
Inverse Degree ◽  
General Randic Index

For a graph G without isolated vertices, the inverse degree of a graph G is defined as I D ( G ) = ∑ u ∈ V ( G ) d ( u ) − 1 where d ( u ) is the number of vertices adjacent to the vertex u in G. By replacing − 1 by any non-zero real number we obtain zeroth-order general Randić index, i.e., 0 R γ ( G ) = ∑ u ∈ V ( G ) d ( u ) γ , where γ ∈ R − { 0 } . Xu et al. investigated some lower and upper bounds on I D for a connected graph G in terms of connectivity, chromatic number, number of cut edges, and clique number. In this paper, we extend their results and investigate if the same results hold for γ < 0 . The corresponding extremal graphs have also been identified.

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