Irregularity Molecular Descriptors of Hourglass, Jagged-Rectangle, and Triangular Benzenoid Systems
Abstract
:1. Introduction
2. Preliminaries and Notations
3. Main Results
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4. Graphical Analysis, Discussions, and Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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Number of Edges | Number of Indices |
---|---|
(2, 2) | |
(2, 3) | |
(3, 3) |
Irregularity Indices | m = 1 | m = 2 | m = 3 | m = 4 | m = 5 |
---|---|---|---|---|---|
0 | 3 | 6 | 9 | 12 | |
0 | 6 | 12 | 18 | 24 | |
0 | 2.4329 | 4.8658 | 7.2987 | 9.7316 | |
0 | 3 | 6 | 9 | 12 | |
0 | 2.44949 | 4.89898 | 7.34847 | 9.79796 | |
0 | 6 | 12 | 18 | 24 | |
0 | 2.40 | 4.80 | 7.20 | 9.60 | |
0 | 4.15888 | 8.31776 | 12.47664 | 16.63552 | |
0 | 0.101022 | 0.202044 | 0.303066 | 0.404088 | |
0 | 0.122465 | 0.244930 | 0.367395 | 0.489860 | |
0 | 0.60612 | 1.21224 | 1.81836 | 2.42448 | |
0 | 3 | 6 | 9 | 12 |
Number of Edges | Number of Indices |
---|---|
(2, 2) | |
(2, 3) | |
(3, 3) |
Irregularity Indices | m = 1 | m = 2 | m = 3 | m = 4 | m = 5 |
---|---|---|---|---|---|
−2 | 4 | 10 | 16 | 22 | |
−4 | 8 | 20 | 32 | 44 | |
−1.62186 | 3.4373 | 8.10932 | 12.97491 | 17.84050 | |
−2 | 4 | 10 | 16 | 22 | |
−1.62992 | 3.265984 | 8.164960 | 13.063936 | 16.962912 | |
−4 | 8 | 20 | 32 | 44 | |
−1.6 | 3.2 | 8.0 | 12.8 | 17.6 | |
−2.772594 | 5.545165 | 13.862925 | 22.18068 | 30.498445 | |
−0.067348 | 0.134696 | 0.336740 | 0.538784 | 0.740828 | |
−0.08158 | 0.16342 | 0.40842 | 0.65342 | 0.89842 | |
−0.40408 | 0.80816 | 2.02040 | 3.23264 | 4.44488 | |
−2 | 4 | 10 | 16 | 22 |
Number of Indices | |
---|---|
(2, 2) | 2 |
(2, 3) | 4 |
(3, 3) | ( |
Irregularity Indices | m = 1 n = 1 | m = 2 n = 2 | m = 3 n = 3 | m = 4 n = 4 | m = 5 n = 5 |
---|---|---|---|---|---|
2 | 6 | 10 | 14 | 18 | |
4 | 12 | 20 | 28 | 36 | |
1.6218043 | 4.865581 | 8.109302 | 11.353023 | 14.596743 | |
2 | 6 | 10 | 14 | 18 | |
1.632993 | 4.898979 | 8.164965 | 11.43095 | 14.696937 | |
4 | 12 | 20 | 28 | 36 | |
1.60 | 4.80 | 8 | 11.20 | 14.40 | |
1.386294 | 4.15888 | 6.931471 | 9.704060 | 12.476649 | |
0.067348 | 0.202044 | 0.336740 | 0.471436 | 0.606132 | |
0.0816439 | 0.244931 | 0.408219 | 0.571507 | 0.734795 | |
0.40408 | 1.21224 | 2.02040 | 2.82856 | 3.636772 | |
2 | 6 | 10 | 14 | 18 |
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Hussain, Z.; Rafique, S.; Munir, M.; Athar, M.; Chaudhary, M.; Ahmad, H.; Min Kang, S. Irregularity Molecular Descriptors of Hourglass, Jagged-Rectangle, and Triangular Benzenoid Systems. Processes 2019, 7, 413. https://doi.org/10.3390/pr7070413
Hussain Z, Rafique S, Munir M, Athar M, Chaudhary M, Ahmad H, Min Kang S. Irregularity Molecular Descriptors of Hourglass, Jagged-Rectangle, and Triangular Benzenoid Systems. Processes. 2019; 7(7):413. https://doi.org/10.3390/pr7070413
Chicago/Turabian StyleHussain, Zafar, Shazia Rafique, Mobeen Munir, Muhammad Athar, Maqbool Chaudhary, Haseeb Ahmad, and Shin Min Kang. 2019. "Irregularity Molecular Descriptors of Hourglass, Jagged-Rectangle, and Triangular Benzenoid Systems" Processes 7, no. 7: 413. https://doi.org/10.3390/pr7070413