scholarly journals More results on extremum Randic indices of (molecular) trees

Filomat ◽  
2018 ◽  
Vol 32 (10) ◽  
pp. 3581-3590 ◽  
Author(s):  
Nor Husin ◽  
Roslan Hasni ◽  
Zhibin Du ◽  
Akbar Ali
Keyword(s):  
Randić Index ◽  
Unicyclic Graphs ◽  
Randic Index ◽  
The Third ◽  
Degree Of Vertex ◽  
Bicyclic Graphs ◽  
Molecular Trees

The Randic index R(G) of a graph G is the sum of the weights (dudv)-1/2 of all edges uv in G, where du denotes the degree of vertex u. Du and Zhou [On Randic indices of trees, unicyclic graphs, and bicyclic graphs, Int. J. Quantum Chem. 111 (2011), 2760-2770] determined the n-vertex trees with the third for n ? 7, the fourth for n ? 10, the fifth and the sixth for n ? 11 maximum Randic indices. Recently, Li et al. [The Randic indices of trees, unicyclic graphs and bicyclic graphs, Ars Comb. 127 (2016), 409-419] obtained the n-vertex trees with the seventh, the eighth, the ninth and the tenth for n ? 11 maximum Randic indices. In this paper, we correct the ordering for the Randic indices of trees obtained by Li et al., and characterize the trees with from the seventh to the sixteenth maximum Randic indices. The obtained extremal trees are molecular and thereby the obtained ordering also holds for molecular trees.

General Randić index of unicyclic graphs with given diameter

2022 ◽  
Vol 306 ◽  
pp. 7-16
Author(s):  
Monther Rashed Alfuraidan ◽  
Kinkar Chandra Das ◽  
Tomáš Vetrík ◽  
Selvaraj Balachandran
Keyword(s):  
Randić Index ◽  
Unicyclic Graphs ◽  
Randic Index ◽  
General Randić Index ◽  
General Randic Index

scholarly journals The minimal total irregularity of some classes of graphs

Filomat ◽  
2016 ◽  
Vol 30 (5) ◽  
pp. 1203-1211 ◽  
Author(s):  
Yingxue Zhu ◽  
Lihua You ◽  
Jieshan Yang
Keyword(s):  
Open Problem ◽  
Vertex Degree ◽  
Connected Graphs ◽  
Unicyclic Graphs ◽  
The Third ◽  
Degree Of A Vertex ◽  
Bicyclic Graphs

In [1], Abdo and Dimitov defined the total irregularity of a graph G=(V,E) as irrt(G)=1/2 ?u,v?V|dG(u)-dG(v)|, where dG(u) denotes the vertex degree of a vertex u ? V. In this paper, we investigate the minimal total irregularity of the connected graphs, determine the minimal, the second minimal, the third minimal total irregularity of trees, unicyclic graphs, bicyclic graphs on n vertices, and propose an open problem for further research.

scholarly journals On a conjecture between Randic index and average distance of unicyclic graphs

Filomat ◽  
2014 ◽  
Vol 28 (4) ◽  
pp. 767-773
Author(s):  
Zhifu You ◽  
Bolian Liu
Keyword(s):  
Average Distance ◽  
Randić Index ◽  
Connected Graphs ◽  
Unicyclic Graphs ◽  
Randic Index

The Randic index R(G) of a graph G is defined as R(G) = ?uv?E (d(u)d(v))-1/2 where the summation goes over all edges of G. In 1988, Fajtlowicz proposed a conjecture: For all connected graphs G with average distance ad(G), then R(G) ? ad(G). In this paper, we prove that this conjecture is true for unicyclic graphs.

scholarly journals Ordering chemical graphs by Sombor indices and its applications

2021 ◽  
Vol 87 (01) ◽  
pp. 5-22
Author(s):  
Hechao Liu ◽  
◽  
Lihua You ◽  
Yufei Huang
Keyword(s):  
Chemical Properties ◽  
Topological Indices ◽  
Unicyclic Graphs ◽  
Degree Of Vertex ◽  
Numerical Invariants ◽  
Tricyclic Graphs ◽  
Bicyclic Graphs ◽  
Physical And Chemical ◽  
And Chemical Properties ◽  
Chemical Trees

Topological indices are a class of numerical invariants that predict certain physical and chemical properties of molecules. Recently, two novel topological indices, named as Sombor index and reduced Sombor index, were introduced by Gutman, defined as where denotes the degree of vertex in . In this paper, our aim is to order the chemical trees, chemical unicyclic graphs, chemical bicyclic graphs and chemical tricyclic graphs with respect to Sombor index and reduced Sombor index. We determine the first fourteen minimum chemical trees, the first four minimum chemical unicyclic graphs, the first three minimum chemical bicyclic graphs, the first seven minimum chemical tricyclic graphs. At last, we consider the applications of reduced Sombor index to octane isomers.

General Randić index of unicyclic graphs with given girth and diameter

2021 ◽  
Author(s):  
Tomáš Vetrík
Keyword(s):  
Lower Bounds ◽  
Randić Index ◽  
Zagreb Index ◽  
Unicyclic Graphs ◽  
Randic Index ◽  
General Randić Index ◽  
General Randic Index ◽  
Modified Zagreb Index

We study the general Randić index of a graph [Formula: see text], [Formula: see text], where [Formula: see text], [Formula: see text] is the edge set of [Formula: see text] and [Formula: see text] and [Formula: see text] are the degrees of vertices [Formula: see text] and [Formula: see text], respectively. For [Formula: see text], we present lower bounds on the general Randić index for unicyclic graphs of given diameter and girth, and unicyclic graphs of given diameter. Lower bounds on the classical Randić index and the second modified Zagreb index are corollaries of our results on the general Randić index.

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