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Combinatorial Chemistry & High Throughput Screening

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ISSN (Print): 1386-2073
ISSN (Online): 1875-5402

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Research Article

Total Irregularity Strengths of an Arbitrary Disjoint Union of (3,6)- Fullerenes

Author(s): Ayesha Shabbir, Muhammad Faisal Nadeem*, Ali Ovais, Faraha Ashraf and Sumiya Nasir

Volume 25, Issue 3, 2022

Published on: 09 December, 2020

Page: [500 - 509] Pages: 10

DOI: 10.2174/1386207323666201209094514

Price: $65

Abstract

Aims and Objective: A fullerene graph is a mathematical model of a fullerene molecule. A fullerene molecule, or simply a fullerene, is a polyhedral molecule made entirely of carbon atoms other than graphite and diamond. Chemical graph theory is a combination of chemistry and graph theory, where theoretical graph concepts are used to study the physical properties of mathematically modeled chemical compounds. Graph labeling is a vital area of graph theory that has application not only within mathematics but also in computer science, coding theory, medicine, communication networking, chemistry, among other fields. For example, in chemistry, vertex labeling is being used in the constitution of valence isomers and transition labeling to study chemical reaction networks

Method: In terms of graphs, vertices represent atoms while edges stand for bonds between the atoms. By tvs (tes) we mean the least positive integer for which a graph has a vertex (edge) irregular total labeling such that no two vertices (edges) have the same weights. A (3,6)-fullerene graph is a non-classical fullerene whose faces are triangles and hexagons

Results: Here, we study the total vertex (edge) irregularity strength of an arbitrary disjoint union of (3,6)-fullerene graphs and provide their exact values.

Conclusion: The lower bound for tvs (tes) depends on the number of vertices. Minimum and maximum degree of a graph exist in literature, while to get different weights, one can use sufficiently large numbers, but it is of no interest. Here, by proving that the lower bound is the upper bound, we close the case for (3,6)-fullerene graphs.

Keywords: (3, 6)-fullerene, disjoint union of graphs, irregularity strength, total vertex irregularity strength, total edge irregularity strength, irregular assignments

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Graphical Abstract

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