Akbar Ali

activity

20142023

most citedA Novel/Old Modification of the First Zagreb Index

95 citations · 322 across the 23 of their papers we have counts for

collaborators

23 papers

math.CO2023

Harmonic-Arithmetic Index of (Molecular) Trees

Abeer M. Albalahi, Akbar Ali, Abdulaziz M. Alanazi +2

Let $G$ be a graph. Denote by $d_{x}$ , $E (G)$ , and $D (G)$ the degree of a vertex $x$ in $G$ , the set of edges of $G$ , and the degree set of $G$ , respectively. This paper proposes to…

math.GM2023★ 17 cited

On the Maximum Atom-Bond Sum-Connectivity Index of Graphs

Tariq Alraqad, Hisham Saber, Akbar Ali +1

The atom-bond sum-connectivity (ABS) index of a graph $G$ with edges $e_{1}, \dots, e_{m}$ is the sum of the numbers $1 - 2 (d_{e_{i}} + 2)^{- 1}$ over $1 \leq i \leq m$ , where $d_{e_{i}}$ is…

math.CO2022★ 2 cited

Minimum Atom-Bond Sum-Connectivity Index of Trees With a Fixed Order and/or Number of Pendent Vertices

Tariq A. Alraqad, Igor Z. Milovanovic, Hicham Saber +3

Let $d_{u}$ be the degree of a vertex $u$ of a graph $G$ . The atom-bond sum-connectivity (ABS) index of a graph $G$ is the sum of the numbers $(1 - 2 (d_{v} + d_{w})^{- 1})^{1/2}$ over all edg…

math.CO2022★ 4 cited

On the Maximum Sigma Index of k-Cyclic Graphs

Akbar Ali, Abeer M. Albalahi, Abdulaziz M. Alanazi +2

Let $G$ be a graph with edge set $E (G)$ . Denote by $d_{w}$ the degree of a vertex $w$ of $G$ . The sigma index of $G$ is defined as $\sum_{uv \in E (G)} (d_{u} - d_{v})^{2}$ . A connected graph o…

math.CO2022★ 5 cited

On the Vertex-Degree-Function Indices of Connected (n,m)-Graphs of Maximum Degree at Most Four

Abeer M. Albalahi, Igor Z. Milovanovic, Zahid Raza +2

Consider a graph $G$ and a real-valued function $f$ defined on the degree set of $G$ . The sum of the outputs $f (d_{v})$ over all vertices $v \in V (G)$ of $G$ is usually known as the v…

math.CO2022

The $k$ -apex trees with minimum augmented Zagreb index

Muhuo Liu, Shumei Pang, Francesco Belardo +1

For a connected graph $G$ on at least three vertices, the augmented Zagreb index (AZI) of $G$ is defined as $$AZI(G)=\sum_{uv\in E(G)}\left(\frac{d(u)d(v)}{d(u)+d(v)-2}\right)^{3},…

math.CO2020★ 10 cited

Towards the Solution of an Extremal Problem Concerning the Wiener Polarity Index of Alkanes

Sadia Noureen, Akhlaq Ahmad Bhatti, Akbar Ali

The Wiener polarity index $W_{p}$ , one of the most studied molecular structure descriptors, was devised by the chemist Harold Wiener for predicting the boiling points of alkanes. The…

math.CO2019★ 5 cited

On the Extremal Zagreb Indices of $n$ -Vertex Chemical Trees with Fixed Number of Segments or Branching Vertices

Sadia Noureen, Akbar Ali, Akhlaq Ahmad Bhatti

Let $C T_{n, k}$ and $C T_{n, b}^{*}$ be the classes of all $n$ -vertex chemical trees with $k$ segments and $b$ branching vertices, respectively, where $3\le k\le n-1…

math.CO2019★ 3 cited

On the Complementary Equienergetic Graphs

Akbar Ali, Suresh Elumalai, Toufik Mansour +1

Energy of a simple graph $G$ , denoted by $E (G)$ , is the sum of the absolute values of the eigenvalues of $G$ . Two graphs with the same order and energy are called equiene…

math.CO2019★ 6 cited

Two Irregularity Measures Possessing High Discriminatory Ability

Akbar Ali, Tamás Réti

An $n$ -vertex graph whose degree set consists of exactly $n - 1$ elements is called antiregular graph. Such type of graphs are usually considered opposite to the regular graphs. An i…

math.CO2019★ 1 cited

A Note on the Modified Albertson Index

Shumaila Yousaf, Akhlaq Ahmad Bhatti, Akbar Ali

The modified Albertson index, denoted by $A^{*}$ , of a graph $G$ is defined as $A^{*} (G) = \sum_{uv \in E (G)} ∣ (d_{u})^{2} - (d_{v})^{2} ∣$ , where $d_{u}$ , $d_{v}$ denote the degrees of…

math.CO2018★ 6 cited

Estimating Some General Molecular Descriptors of Saturated Hydrocarbons

Akbar Ali, Zhibin Du, Kiran Shehzadi

Three general molecular descriptors, namely the general sum-connectivity index, general Platt index and ordinary generalized geometric-arithmetic index, are studied here. Best poss…

math.CO2018

A note on polyomino chains with extremum general sum-connectivity index

Akbar Ali, Tahir Idrees

The general sum-connectivity index of a graph $G$ is defined as $χ_{α} (G) = \sum_{uv \in E (G)} (d_{u} + d_{v})^{α}$ where $d_{u}$ is degree of the vertex $u \in V (G)$ , $α$ is a real number…

math.CO2017★ 5 cited

On the zeroth-order general Randić index, variable sum exdeg index and trees having vertices with prescribed degree

Sohaib Khalid, Akbar Ali

The zeroth-order general Randić index (usually denoted by $R_{α}^{0}$ ) and variable sum exdeg index (denoted by $S E I_{a}$ ) of a graph $G$ are defined as $R_α^{0}(G)= \sum_{v\in V(G)}…

math.CO2017★ 56 cited

On the Extremal Graphs with Respect to Bond Incident Degree Indices

Akbar Ali, Darko Dimitrov

Many existing degree based topological indices can be classified as bond incident degree (BID) indices, whose general form is $B I D (G) = \sum_{uv \in E (G)}$ $Ψ (d_{u}, d_{v})$ , where $uv…

math.CO2017★ 95 cited

A Novel/Old Modification of the First Zagreb Index

Akbar Ali, Nenad Trinajstić

In the paper [I. Gutman, N. Trinajstić, Chem. Phys. Lett. 17 (1972), 535], it was shown that total $π$ -electron energy ( $E$ ) of a molecule $M$ depends on the quantity $\sum_{v\in V…

math.CO2016★ 9 cited

Extremal Triangular Chain Graphs for Bond Incident Degree (BID) Indices

Akbar Ali, Akhlaq Ahmad Bhatti

A general expression for calculating the bond incident degree (BID) indices of certain triangular chain graphs is derived. The extremal triangular chain graphs with respect to seve…

math.CO2016★ 16 cited

A note on the augmented Zagreb index of cacti with fixed number of vertices and cycles

Akbar Ali, Akhlaq Ahmad Bhatti

Let $C_{n, k}$ be the family of all cacti with $k$ cycles and $n \geq 4$ vertices. In the present note, the element of the class $C_{n, k}$ having minimum augmented…

math.CO2016★ 2 cited

A note on the minimum reduced reciprocal Randić index of n-vertex unicyclic graphs

Akbar Ali, Akhlaq Ahmad Bhatti

The graph having the minimum reduced reciprocal Randić index is characterized among the class of all unicyclic graphs with fixed number of vertices.

math.CO2015★ 26 cited

Bond Incident Degree (BID) Indices of Polyomino Chains: A Unified Approach

A. Ali, Z. Raza, A. A. Bhatti

This work is devoted to establish a general expression for calculating the bond incident degree (BID) indices of polyomino chains and to characterize the extremal polyomino chains…

math.CO2014★ 23 cited

On the Augmented Zagreb Index

Akbar Ali, Zahid Raza, Akhlaq Ahmad Bhatti

Topological indices play an important role in mathematical chemistry especially in the quantitative structure-property relationship (QSPR) and quantitative structure-activity relat…

math.CO2014★ 16 cited

Further Inequalities Between Vertex-Degree-Based Topological Indices

Akbar Ali, Akhlaq Ahmad Bhatti, Zahid Raza

Continuing the recent work of L. Zhong and K. Xu [MATCH Commun. Math. Comput. Chem.71(2014) 627-642], we determine inequalities among several vertex-degree-based topological indice…

math.CO2014★ 15 cited

More on Comparison Between First Geometric-Arithmetic Index and Atom-Bond Connectivity Index

Zahid Raza, Akhlaq Ahmad Bhatti, Akbar Ali

The first geometric-arithmetic (GA) index and atom-bond connectivity (ABC) index are molecular structure descriptors which play a significant role in quantitative structure-propert…

Harmonic-Arithmetic Index of (Molecular) Trees

On the Maximum Atom-Bond Sum-Connectivity Index of Graphs

Minimum Atom-Bond Sum-Connectivity Index of Trees With a Fixed Order and/or Number of Pendent Vertices

On the Maximum Sigma Index of k-Cyclic Graphs

On the Vertex-Degree-Function Indices of Connected (n,m)-Graphs of Maximum Degree at Most Four

The k-apex trees with minimum augmented Zagreb index

Towards the Solution of an Extremal Problem Concerning the Wiener Polarity Index of Alkanes

On the Extremal Zagreb Indices of n-Vertex Chemical Trees with Fixed Number of Segments or Branching Vertices

On the Complementary Equienergetic Graphs

Two Irregularity Measures Possessing High Discriminatory Ability

A Note on the Modified Albertson Index

Estimating Some General Molecular Descriptors of Saturated Hydrocarbons

A note on polyomino chains with extremum general sum-connectivity index

On the zeroth-order general Randić index, variable sum exdeg index and trees having vertices with prescribed degree

On the Extremal Graphs with Respect to Bond Incident Degree Indices

A Novel/Old Modification of the First Zagreb Index

Extremal Triangular Chain Graphs for Bond Incident Degree (BID) Indices

A note on the augmented Zagreb index of cacti with fixed number of vertices and cycles

A note on the minimum reduced reciprocal Randić index of n-vertex unicyclic graphs

Bond Incident Degree (BID) Indices of Polyomino Chains: A Unified Approach

On the Augmented Zagreb Index

Further Inequalities Between Vertex-Degree-Based Topological Indices

More on Comparison Between First Geometric-Arithmetic Index and Atom-Bond Connectivity Index

The $k$ -apex trees with minimum augmented Zagreb index

On the Extremal Zagreb Indices of $n$ -Vertex Chemical Trees with Fixed Number of Segments or Branching Vertices