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.

Remark on upper bounds of Randi´c index of a graph

2016 ◽  
Vol 25 (1) ◽  
pp. 71-75
Author(s):  
I. Z. MILOVANOVIC ◽  
◽  
P. M. BEKAKOS ◽  
M. P. BEKAKOS ◽  
E. I. MILOVANOVIC ◽  
...  
Keyword(s):  
Upper Bound ◽  
Degree Sequence ◽  
Upper Bounds ◽  
Simple Graph ◽  
Vertex Degree ◽  
Randić Index ◽  
Randic Index ◽  
General Randić Index ◽  
General Randic Index

Let G = (V, E) be an undirected simple graph of order n with m edges without isolated vertices. Further, let d1 ≥ d2 ≥ · · · ≥ dn be vertex degree sequence of G. General Randic index of graph ´ G = (V, E) is defined by Rα = X (i,j)∈E (didj ) α, where α ∈ R − {0}. We consider the case when α = −1 and obtain upper bound for R−1.

scholarly journals On the Number of Spanning Trees of Graphs

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
Ş. Burcu Bozkurt ◽  
Durmuş Bozkurt
Keyword(s):  
Spanning Trees ◽  
Vertex Degree ◽  
Randić Index ◽  
First Zagreb Index ◽  
Zagreb Index ◽  
Connected Graphs ◽  
Randic Index ◽  
Number Of Spanning Trees

We establish some bounds for the number of spanning trees of connected graphs in terms of the number of vertices(n), the number of edges(m), maximum vertex degree(Δ1), minimum vertex degree(δ),…first Zagreb index(M1),and Randić index(R-1).

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

scholarly journals On the Randić Index of Corona Product Graphs

2011 ◽  
Vol 2011 ◽  
pp. 1-7
Author(s):  
Ismael G. Yero ◽  
Juan A. Rodríguez-Velázquez
Keyword(s):  
Degree Sequence ◽  
Upper Bounds ◽  
Vertex Degree ◽  
Regular Graphs ◽  
Randić Index ◽  
Lower And Upper Bounds ◽  
Randic Index ◽  
Product Graphs ◽  
Vertex Set ◽  
Corona Product

Let G be a graph with vertex set V=(v1,v2,…,vn). Let δ(vi) be the degree of the vertex vi∈V. If the vertices vi1,vi2,…,vih+1 form a path of length h≥1 in the graph G, then the hth order Randić index Rh of G is defined as the sum of the terms 1/δ(vi1)δ(vi2)⋯δ(vih+1) over all paths of length h contained (as subgraphs) in G. Lower and upper bounds for Rh, in terms of the vertex degree sequence of its factors, are obtained for corona product graphs. Moreover, closed formulas are obtained when the factors are regular graphs.

scholarly journals Topological Indices of Dendrimers used in Drug Delivery

2020 ◽  
Vol 12 (4) ◽  
pp. 645-655
Author(s):  
T. P. Jude ◽  
E. Panchadcharam ◽  
K. Masilamani
Keyword(s):  
Drug Delivery ◽  
Molecular Graph ◽  
Topological Indices ◽  
Vertex Degree ◽  
Numerical Representation ◽  
Chemical Bonds ◽  
Randić Index ◽  
Zagreb Index ◽  
Randic Index ◽  
Carrier Vehicle

The topological index is a numerical representation of a molecular structure. In chemical graphs, the atoms and the chemical bonds between them are represented by vertices and edges respectively. Vertex degree based topological indices are the most studied and mostly used type of topological indices. The mostly used vertex degree based topological indices in the field of drug design and developments are the Zagreb index and the Randić index. The structural chemistry of dendrimers could be manipulated by their topological indices to get the specific structure with required properties to deliver the drugs to target carrier vehicle. In this work, topological indices of three types of dendrimers which are used as the drug delivery system were studied and their Zagreb index and the Randić index were calculated using molecular graph theory. Moreover, the other versions of these two indices were also calculated to these dendrimers.

scholarly journals Some inequalities for general zeroth-order Randic index

Filomat ◽  
2019 ◽  
Vol 33 (16) ◽  
pp. 5249-5258
Author(s):  
Predrag Milosevic ◽  
Igor Milovanovic ◽  
Emina Milovanovic ◽  
Marjan Matejic
Keyword(s):  
Connected Graph ◽  
Degree Sequence ◽  
Vertex Degree ◽  
Arbitrary Real Number ◽  
Randić Index ◽  
Zeroth Order ◽  
Real Numbers ◽  
Randic Index ◽  
Simple Connected Graph ◽  
New Inequalities

Let G=(V,E), V={v1, v2,..., vn}, be a simple connected graph with n vertices, m edges and vertex degree sequence ? = d1?d2 ?...? dn = ? > 0, di = d(vi). General zeroth-order Randic index of G is defined as 0R?(G) = ?ni =1 d?i , where ? is an arbitrary real number. In this paper we establish relationships between 0R?(G) and 0R?-1(G) and obtain new bounds for 0R?(G). Also, we determine relationship between 0R?(G), 0R?(G) and 0R2?-?(G), where ? and ? are arbitrary real numbers. By the appropriate choice of parameters ? and ?, a number of old/new inequalities for different vertex-degree-based topological indices are obtained.

scholarly journals Gibbs Random Fields with Unbounded Spins on Unbounded Degree Graphs

2010 ◽  
Vol 47 (03) ◽  
pp. 856-875
Author(s):  
Yuri Kondratiev ◽  
Yuri Kozitsky ◽  
Tanja Pasurek
Keyword(s):  
Random Fields ◽  
Large Degree ◽  
Vertex Degree ◽  
Uniform Integrability ◽  
Randić Index ◽  
Topological Properties ◽  
Anharmonic Oscillators ◽  
Randic Index ◽  
Gibbs Fields ◽  
Gibbs Random Fields

Gibbs fields are constructed and studied which correspond to systems of real-valued spins (e.g. systems of interacting anharmonic oscillators) indexed by the vertices of unbounded degree graphs of a certain type, for which the Gaussian Gibbs fields need not be existing. In these graphs, the vertex degree growth is controlled by a summability requirement formulated with the help of a generalized Randić index. In particular, it is proven that the Gibbs fields obey uniform integrability estimates, which are then used in the study of the topological properties of the set of Gibbs fields. In the second part, a class of graphs is introduced in which the mentioned summability is obtained by assuming that the vertices of large degree are located at large distances from each other. This is a stronger version of the metric property employed in Bassalygo and Dobrushin (1986).

Four New/Old Vertex-Degree-Based Topological Indices of HAC5C7[p, q] and HAC5C6C7[p, q] Nanotubes

2017 ◽  
Vol 14 (1) ◽  
pp. 796-799 ◽  
Author(s):  
Yingfang Li ◽  
Li Yan ◽  
Muhammad Kamran Jamil ◽  
Mohammad Reza Farahani ◽  
Wei Gao ◽  
...  
Keyword(s):  
Topological Indices ◽  
Vertex Degree ◽  
Randić Index ◽  
Zagreb Index ◽  
Randic Index ◽  
Second Zagreb Index ◽  
Forgotten Index ◽  
Mathematical Literature

Recently, Gutman et al. presented some vertex-degree based topological indices, that earlier have been considered in the chemical and/or mathematical literature, but, evaded the attention of most mathematical chemists. These are the reciprocal Randic index (RR), the reduced reciprocal Randic index (RRR), the reduced second Zagreb index (RM2) and the forgotten index (F). In this paper, we compute these topological indices of HAC5C7[p, q] and HAC5C6C7[p, q] nanotubes.

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