On M-Polynomials of Dunbar Graphs in Social Networks
Abstract
:1. Introduction
2. Defining Network Structure as M-Polynomial
2.1. The -Agent Recruitment Graph
2.2. Topological Indices From The M-polynomial
3. Dunbar Graphs and Topological Indices
4. Discussion
5. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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Topological Index | Notion for Topological Index | Derivation from or |
---|---|---|
First Zagreb | ||
Second Zagreb | ( | |
Second modified Zagreb | ||
General Randi | ||
General Inverse Randi | ||
Symmetric Division Index | ||
Harmonic Index | H(G) | 2 |
Inverse sum Index | I(G) | |
Augmented Zagreb Index | AZI(G) |
1 | m | ||
---|---|---|---|
Number of vertices | 1 |
(1, ) | (m, ) | (, ) | |
---|---|---|---|
Number of edges | m |
(5,5,6) | 156,230 | 234,300 | 2712.6667 | 96,364.333 | 5115.1948 | 5115.1948 | 13,406.494 |
(5,150,6) | 5.848 | 1.154 | 2.515 | 5.734 | 5.013 | 3.772 | 3.873. |
(5,5,4) | 6230 | 9300 | 108.5 | 3864.3333 | 204.48052 | 549.35065 | 1265.1852 |
(5,150,4) | 2.599 | 5.130 | 111759.94 | 2.548 | 222,789.54 | 16,764,004 | 17,215,344 |
(150,150,6) | 1.754 | 3.463 | 7.544 | 1.720 | 1.504 | 1.132 | 1.162 |
(150,150,4) | 7.798 | 1.539 | 3352798 | 7.645 | 6,683,685.2 | 5.029 | 5.816 |
(150,5,6) | 470,8650 | 715,9500 | 81,375.167 | 2,894,381 | 153,430.49 | 402,651.1 | 839,940.33 |
(150,5,4) | 208,650 | 409,500 | 3250.1667 | 11,9381 | 6109.0659 | 16,936.813 | 62,340.333 |
(5,15,6) | 73,225,380 | 1.302 | 238,364.12 | 60,987,322 | 463,641.65 | 357,3548.5 | 4,608,373.2 |
(5,15,4) | 325,380 | 577,600 | 1059.4375 | 271,072 | 2060.7703 | 15,901.401 | 20,853.232 |
(15,5,6) | 468,840 | 703,800 | 8137.6667 | 289,106 | 15,344.286 | 40,242.857 | 82,594.256 |
(15,5,4) | 18,840 | 28,800 | 325.16667 | 11,606 | 612.14286 | 1671.4286 | 4834.2557 |
(15,15,6) | 2.197 | 3.905 | 715,092.25 | 1.830 | 1,390,924.5 | 10,720,704 | 13,832,502 |
(15,15,4) | 976,290 | 1,735,200 | 3178.1875 | 813,194.12 | 6181.8501 | 47,763.188 | 69,942.194 |
(15,150,6) | 1.754 | 3.463 | 7.544 | 1.720 | 1.504 | 1.132 | 1.162. |
(15,150,4) | 7.798 | 1.539 | 35,279.81 | 7.645 | 668,368.6 | 50,292,145 | 51,683,780 |
15,625 + 56 + 3900 | 15625 + 56 + 3900 | ||||||
3.797 + 5151 + 2.548 | 3.797 + 5151 + 2.548 | ||||||
625 + 56 + 150 | 625 + 56 + 150 | ||||||
16,875,000 + 5151 + 113,250 | 16,875,000 + 5151 + 113,250 | ||||||
1.139 + 150151 + 7.645 | 1.139 + 150151 + 7.645 | ||||||
5.062 + 150151 + 3,397,500 | 5.062 + 150151 + 3,397,500 | ||||||
468,750 + 1506 + 117,000 | 468,750 + 1506 + 117,000 | ||||||
18,750 + 1506 + 4500 | 18,750 + 1506 + 4500 | ||||||
3796875 + 516 + 271,200 | 3,796,875 + 516 + 271,200 | ||||||
16,875 + 516 + 1200 | 16,875 + 516 + 1200 | ||||||
46,875 + 156 + 11,700 | 46,875 + 156 + 11,700 | ||||||
1875 + 156 + 450 | 1875 + 156 + 450 | ||||||
11,390,625 + 1516 + 813,600 | 11,390,625 + 1516 + 813,600 | ||||||
50,625 + 1516 + 3600 | 50,625 + 1516 + 3600 | ||||||
1.139 + 15151 + 7.645 | 1.139 + 15151 + 7.645, | ||||||
50,625,000 + 15151 + 339,750 | 50,625,000 + 15151 + 339,750, |
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Acharjee, S.; Bora, B.; Dunbar, R.I.M. On M-Polynomials of Dunbar Graphs in Social Networks. Symmetry 2020, 12, 932. https://doi.org/10.3390/sym12060932
Acharjee S, Bora B, Dunbar RIM. On M-Polynomials of Dunbar Graphs in Social Networks. Symmetry. 2020; 12(6):932. https://doi.org/10.3390/sym12060932
Chicago/Turabian StyleAcharjee, Santanu, Bijit Bora, and Robin I. M. Dunbar. 2020. "On M-Polynomials of Dunbar Graphs in Social Networks" Symmetry 12, no. 6: 932. https://doi.org/10.3390/sym12060932
APA StyleAcharjee, S., Bora, B., & Dunbar, R. I. M. (2020). On M-Polynomials of Dunbar Graphs in Social Networks. Symmetry, 12(6), 932. https://doi.org/10.3390/sym12060932