scholarly journals On atom-bond connectivity index

Filomat ◽  
2012 ◽  
Vol 26 (4) ◽  
pp. 733-738 ◽  
Author(s):  
Kinkar Das ◽  
Ivan Gutman ◽  
Boris Furtula
Keyword(s):  
Upper Bounds ◽  
Connectivity Index ◽  
Vertex Degree ◽  
Graph Invariant ◽  
Atom Bond

The atom-bond connectivity index (ABC) is a vertex-degree based graph invariant, put forward in the 1990s, having applications in chemistry. Let G = (V,E) be a graph, di the degree of its vertex i, and ij the edge connecting the vertices i and j. Then ABC = ?ij?E ?(di+dj?2)/(didj). Upper bounds and Nordhaus-Gaddum type results for ABC are established.

scholarly journals Some upper bounds for the atom–bond connectivity index of graphs

2012 ◽  
Vol 25 (7) ◽  
pp. 1077-1081 ◽  
Author(s):  
Jinsong Chen ◽  
Jianping Liu ◽  
Xiaofeng Guo
Keyword(s):  
Upper Bounds ◽  
Connectivity Index ◽  
Atom Bond

scholarly journals Investigation of General Power Sum-Connectivity Index for Some Classes of Extremal Graphs

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Rui Cheng ◽  
Gohar Ali ◽  
Gul Rahmat ◽  
Muhammad Yasin Khan ◽  
Andrea Semanicova-Fenovcikova ◽  
...  
Keyword(s):  
Connected Graph ◽  
Topological Index ◽  
Upper Bounds ◽  
Connectivity Index ◽  
Extremal Graphs ◽  
Graph Invariant ◽  
Power Sum ◽  
General Power

In this work, we introduce a new topological index called a general power sum-connectivity index and we discuss this graph invariant for some classes of extremal graphs. This index is defined by Y α G = ∑ u v ∈ E G d u d u + d v d v α , where d u and d v represent the degree of vertices u and v , respectively, and α ≥ 1 . A connected graph G is called a k -generalized quasi-tree if there exists a subset V k ⊂ V G of cardinality k such that the graph G − V k is a tree but for any subset V k − 1 ⊂ V G of cardinality k − 1 , the graph G − V k − 1 is not a tree. In this work, we find a sharp lower and some sharp upper bounds for this new sum-connectivity index.

On Atom-Bond Connectivity Index

2011 ◽  
Vol 66 (1-2) ◽  
pp. 61-66 ◽  
Author(s):  
Bo Zhou ◽  
Rundan Xing
Keyword(s):  
Upper Bounds ◽  
Graph Invariant ◽  
Excellent Correlation ◽  
First Zagreb Index ◽  
Zagreb Index ◽  
The Third ◽  
Connectivity Indices ◽  
Abc Index ◽  
The First Zagreb Index ◽  
Atom Bond

The atom-bond connectivity (ABC) index, introduced by Estrada et al. in 1998, displays an excellent correlation with the formation heat of alkanes. We give upper bounds for this graph invariant using the number of vertices, the number of edges, the Randi´c connectivity indices, and the first Zagreb index. We determine the unique tree with the maximum ABC index among trees with given numbers of vertices and pendant vertices, and the n-vertex trees with the maximum, and the second, the third, and the fourth maximum ABC indices for n ≥ 6.

scholarly journals Some inequalities for the atom-bond connectivity index of graph operations

2011 ◽  
Vol 159 (13) ◽  
pp. 1323-1330 ◽  
Author(s):  
G.H. Fath-Tabar ◽  
B. Vaez-Zadeh ◽  
A.R. Ashrafi ◽  
A. Graovac
Keyword(s):  
Connectivity Index ◽  
Graph Operations ◽  
Atom Bond

scholarly journals Upper bounds on the energy of graphs in terms of matching number

2021 ◽  
pp. 16-16
Author(s):  
Saieed Akbari ◽  
Abdullah Alazemi ◽  
Milica Andjelic
Keyword(s):  
Adjacency Matrix ◽  
Connected Graph ◽  
Short Proof ◽  
Upper Bounds ◽  
Vertex Degree ◽  
Maximum Matching ◽  
Matching Number ◽  
Open Problems

The energy of a graph G, ?(G), is the sum of absolute values of the eigenvalues of its adjacency matrix. The matching number ?(G) is the number of edges in a maximum matching. In this paper, for a connected graph G of order n with largest vertex degree ? ? 6 we present two new upper bounds for the energy of a graph: ?(G) ? (n-1)?? and ?(G) ? 2?(G)??. The latter one improves recently obtained bound ?(G) ? {2?(G)?2?e + 1, if ?e is even; ?(G)(? a + 2?a + ?a-2?a), otherwise, where ?e stands for the largest edge degree and a = 2(?e + 1). We also present a short proof of this result and several open problems.

scholarly journals On Atom-Bond Connectivity Index

2011 ◽  
Vol 66a ◽  
pp. 61 ◽  
Author(s):  
Zhou B. ◽  
Xing R.
Keyword(s):  
Connectivity Index ◽  
Atom Bond

scholarly journals More on comparison between first geometric-arithmetic index and atom-bond connectivity index

2016 ◽  
Vol 17 (1) ◽  
pp. 561 ◽  
Author(s):  
Zahid Raza ◽  
Akhlaq Ahmad Bhatti ◽  
Akbar Ali
Keyword(s):  
Connectivity Index ◽  
Atom Bond

scholarly journals Vertex-Based Topological Indices of Double and Strong Double Graph of Dutch Windmill Graph

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Muhammad Asad Ali ◽  
Muhammad Shoaib Sardar ◽  
Imran Siddique ◽  
Dalal Alrowaili
Keyword(s):  
Graph Theory ◽  
Chemical Properties ◽  
Topological Indices ◽  
Connectivity Index ◽  
Vaporization Enthalpy ◽  
Zagreb Index ◽  
Graph Operations ◽  
Big Graphs ◽  
Physical And Chemical ◽  
Atom Bond

A measurement of the molecular topology of graphs is known as a topological index, and several physical and chemical properties such as heat formation, boiling point, vaporization, enthalpy, and entropy are used to characterize them. Graph theory is useful in evaluating the relationship between various topological indices of some graphs derived by applying certain graph operations. Graph operations play an important role in many applications of graph theory because many big graphs can be obtained from small graphs. Here, we discuss two graph operations, i.e., double graph and strong double graph. In this article, we will compute the topological indices such as geometric arithmetic index GA , atom bond connectivity index ABC , forgotten index F , inverse sum indeg index ISI , general inverse sum indeg index ISI α , β , first multiplicative-Zagreb index PM 1   and second multiplicative-Zagreb index PM 2 , fifth geometric arithmetic index GA 5 , fourth atom bond connectivity index ABC 4 of double graph, and strong double graph of Dutch Windmill graph D 3 p .

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