[HTML][HTML] Geometric perspective to degree–based topological indices of supramolecular chain

M Imran, R Luo, MK Jamil, M Azeem, KM Fahd - Results in Engineering, 2022 - Elsevier
Sombor index and their types are introduced pertaining to Euclidean geometry. In graph-
theoretical terminology, it is the sum of all pairs of adjacent vertices di 2+ dj 2 given di is the …

[HTML][HTML] Entropy measures of Y-junction based nanostructures

ANA Koam, M Azeem, MK Jamil, A Ahmad… - Ain Shams Engineering …, 2023 - Elsevier
Recent research on nanostructures proved their importance and implementation in various
areas. In drug delivery systems, medicine and pharmaceutical, biological sensors …

Sombor topological indices for different nanostructures

M Imran, R Ismail, M Azeem, MK Jamil, EHA Al-Sabri - Heliyon, 2023 - cell.com
Euclidean geometry is utilized to establish the Sombor graph parameter and its invariants. It
is sum of all adjacent vertices in graph theory d ϒ 2+ d Γ 2 where d ϒ is the degree of the …

[PDF][PDF] Computing Connected Resolvability of Graphs Using Binary Enhanced Harris Hawks Optimization.

B Mohamed, L Mohaisen, M Amin - Intelligent Automation & Soft …, 2023 - researchgate.net
In this paper, we consider the NP-hard problem of finding the minimum connected resolving
set of graphs. A vertex set B of a connected graph G resolves G if every vertex of G is …

[HTML][HTML] The metric dimension of the circulant graph with 2k generators can be less than k

T Vetrík, M Imran, M Knor, R Škrekovski - Journal of King Saud University …, 2023 - Elsevier
Circulant graphs are useful networks because of their symmetries. For k⩾ 2 and n⩾ 2 k+ 1,
the circulant graph C n (1, 2,…, k) consists of the vertices v 0, v 1, v 2,…, v n-1 and the edges …

[HTML][HTML] Topological properties of reverse-degree-based indices for sodalite materials network

ANA Koam, MA Ansari, A Haider, A Ahmad… - Arabian Journal of …, 2022 - Elsevier
Natural zeolites are frequently referred to as macromolecular sieves. Because of relatively
inexpensive cost of installation, zeolites networks are highly trendy chemical networks …

Sombor indices of γ-sheet of boron clusters

EA Refaee, A Ahmad, M Azeem - Molecular Physics, 2023 - Taylor & Francis
Regarding Euclidean geometry, introduced the Sombor index and its various types. In graph
theory, it is the sum of all pairs of neighbouring vertices. New varieties of Sombor indices are …

Computing the partition dimension of certain families of Toeplitz graph

R Luo, A Khalil, A Ahmad, M Azeem… - Frontiers in …, 2022 - frontiersin.org
Let G=(V (G), E (G)) be a graph with no loops, numerous edges, and only one component,
which is made up of the vertex set V (G) and the edge set E (G). The distance d (u, v) …

[PDF][PDF] Comparative study of vertex-edge based indices for semi-capped carbon nanotubes

Q Huang, A Ahmad, MK Jamil, R Luo… - Mathematical …, 2022 - aimspress.com
Manufacturing relatively inexpensive items in every area of engineering and science is the
major focus of exploration resultant the world's contemporary economic setback. Making …

Sharp Lower Bound of Cacti Graph with respect to Zagreb Eccentricity Indices

A Alamer, KH Hakami, MR Rahimi… - Journal of …, 2024 - Wiley Online Library
The first Zagreb eccentricity index E1 (℧) is the sum of square of eccentricities of the vertices,
and the second Zagreb eccentricity index E2 (℧) is the sum of product squares of the …