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Mathematics 2018, 6(9), 150; https://doi.org/10.3390/math6090150

Computing The Irregularity Strength of Planar Graphs

1
School of Information Science and Engineering, Chengdu University, Chengdu 610106, China
2
Department of Mathematics, COMSATS University Islamabad, Sahiwal Campus, Sahiwal 57000, Pakistan
3
Center for Advanced Studies in Pure and Applied Mathematics, Bahauddin Zakariya University Multan, Multan 60800, Pakistan
4
Department of Mathematics, COMSATS University Islamabad, Lahore Campus, Lahore 54000, Pakistan
5
College of Computer Science & Information Systems, Jazan University, Jazan 45142, Saudi Arabia
*
Author to whom correspondence should be addressed.
Received: 23 July 2018 / Revised: 25 August 2018 / Accepted: 27 August 2018 / Published: 30 August 2018
(This article belongs to the Special Issue Discrete Optimization: Theory, Algorithms, and Applications)
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Abstract

The field of graph theory plays a vital role in various fields. One of the important areas in graph theory is graph labeling used in many applications such as coding theory, X-ray crystallography, radar, astronomy, circuit design, communication network addressing, and data base management. In this paper, we discuss the totally irregular total k labeling of three planar graphs. If such labeling exists for minimum value of a positive integer k, then this labeling is called totally irregular total k labeling and k is known as the total irregularity strength of a graph G. More preciously, we determine the exact value of the total irregularity strength of three planar graphs. View Full-Text
Keywords: total edge irregularity strength; total vertex irregularity strength; total irregularity strength; planar graph total edge irregularity strength; total vertex irregularity strength; total irregularity strength; planar graph
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).
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Yang, H.; Siddiqui, M.K.; Ibrahim, M.; Ahmad, S.; Ahmad, A. Computing The Irregularity Strength of Planar Graphs. Mathematics 2018, 6, 150.

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