The study of the b-choromatic number of some classes of fractal graphs

References

• R.J. Wilson. Introduction to Graph Theory, John Wiley and Sons, Inc.605 Third Ave. New York, NYUnited States,1986. https://dl.acm.org/doi/10.5555/22577
   Google Scholar
• B. Bollobas, Modern graph theory, volume 184 of Graduate Texts in Mathematics. Springer-Verlag, 1998. https://link.springer.com/book/10.1007/978-1-4612-0619-4
   Google Scholar
• B. Tosuni, Graph Coloring Problems in Modern Computer Science, European Journal of Interdis-ciplinary Studies, 1(2), (2015), 87-95. https://doi.org/10.26417/ejis.v1i2.p87-95
   Google Scholar
• M. D. Barrus, S. G. Hartke and M. Kumbhat, Graph Classes Characterized Both by For-bidden Subgraphs and Degree Sequences. Journal of Graph Theory, 57(2), 2005, 131-148. https://dl.acm.org/doi/abs/10.5555/1330411.1330414
   Google Scholar
• S. Corteela, M. Valencia-PabonbJuan, C. Verac, On approximating the b-chromatic number, Discrete Applied Mathematics, 146(1), (2005), 106-110. doi: 10.1016/j.dam.2004.09.006
   Web of Science ®Google Scholar
• D. Vijayalakshmi, K. Thilagavathi, N. Roopesh, The b-chromatic number of M[Cn], M[Pn], M[Fn] and M[Wn], Open journal of Discrete Mathematics, 1(2), (2011), 85. https://doi.org/10.4236/ojdm.2011.12010
   Google Scholar
• R.W. Irving, David F. Manlove, The b-chromatic number of a graph, Discrete Applied Mathematics, 91(1-3), (1999), 127-141. https://doi.org/10.1016/S0166-218X(98)00146-2
   Web of Science ®Google Scholar
• M. Jakovac, S. Klavzar, The b-chromatic number of cubic graphs, Graphs and Combinatories, 26(1)(2010), 107-118. https://doi.org/10.1007/s00373-010-0898-9
   Google Scholar
• V. Vivin, The b-chromatic number of corona graphs, Utilitas Mathematica, 88, (2012), 299-307. https://www.semanticscholar.org/paper/The-b-Chromatic-Number-of-Corona-Graphs-Vivin/29c956719a401dfb8369045c5dfaae50023cbdb3
   Web of Science ®Google Scholar
• R.S. Scorer, P. M. Grundy, C. A. B. Smith, Some binary games, Math. Gaz. 28 (1944) 96-103. doi: 10.2307/3606393
   Google Scholar
• M. Kouider, M. Maheo, Some bounds for the b-chromatic number of a graph, Discrete Mathematics, 256(1-2), (2002), 267-277. https://doi.org/10.1016/S0012-365X(01)00469-1
   Web of Science ®Google Scholar
• R. Nagarathinam, N. Parvathi, On b-coloring line, middle and total graph of tadpole graph, In AIP Conference Proceedings, 2277(1) (2020), (1-4). https://doi.org/10.1063/5.0026012
   Google Scholar
• S.K. Vaidya, Rakhimol V. Isaac, The b-chromatic number of some path related graphs, International Journal of Mathematics and Scientific Computing, 4(1), (2014), 7-12. https://www.veltech.edu.in/wp-content/uploads/2016/04/Paper-03-14.pdf
   Google Scholar
• J. Vernold Vivin, M. Vekatachalamb, On b-chromatic number of sun let graph and wheel graph families, Journal of the Egyptian Mathematical Society, 23(2), 215-218. https://doi.org/10.1016/j.joems.2014.05.011
   Google Scholar
• P. Skums, Graph fractal dimension and the structure of fractal networks, Journal of Complex Networks, 8(4), (2020), 037. https://doi.org/10.1093/comnet/cnaa037
   Web of Science ®Google Scholar
• Z. Jiang, W. Yan, Some Two-Point Resistances of the Sierpinski Gasket Network. J Stat Phys., 172, 824-832 (2018). https://doi.org/10.1007/s10955-018-2067-0
   Web of Science ®Google Scholar
• A.R. Nizami, K. Shabbir, M.S. Sardar, M. Qasim, M. Cancan, S. Ediz. Base polynomials for degree and distance based topological invariants of n-bilinear straight pentachain Journal of Information and Optimization Sciences, 8, (2021) https://doi.org/10.1080/02522667.2021.1903202
   Google Scholar
• M.S. Sardar, M. Alaeiyan, M.R. Farahani, M. Cancan, S. Ediz. Resistance distance in some classes of rooted product graphs obtained by Laplacian generalized inverse method, Journal of Information and Optimization Sciences, 42(7), 2021. 1447-1467. https://doi.org/10.1080/02522667.2021.1899210
   Web of Science ®Google Scholar
• Z. Ahmad, M.A. Chaudhary, A.Q. Baig, M.A. Zahid, On metric dimension of P(n; 2)K1 graph. Journal of Discrete Mathematical Sciences and Cryptography. 24(2), 2021. 629-645. https://doi.org/10.1080/09720529.2021.1907017
   Web of Science ®Google Scholar
• Z. Ahmad, M.A. Chaudhary, A. Q.r Baig, M.A. Zahid. Fault-tolerant metric dimension of P(n; 2) K1 graph, Journal of Discrete Mathematical Sciences and Cryptography. 24(2), 2021. 647-656. https://doi.org/10.1080/09720529.2021.1899209
   Web of Science ®Google Scholar
• W. Sajjad, M. Shoaib Sardar, M. Cancan, S. Ediz, A.Q. Baig. On modified eccentric connectiv-ity index of nanotube, Journal of Information and Optimization Sciences, 41(4), 2020, 959-972. https://doi.org/10.1080/02522667.2020.1745380
   Web of Science ®Google Scholar
• M.S. Sardar, S.-A. Xu, W. Sajjad, S. Zafar, I.N. Cangul, M.R. Farahani. An explicit formula for the harmonic indices and harmonic polynomials of carbon nanocones CNC k [n], Journal of Information and Optimization Sciences, 41(4), 2020, 879-890. https://doi.org/10.1080/02522667.2020.1753304
   Web of Science ®Google Scholar
• A. Amer, M. Naeem, H. Ur Rehman, M. Irfan, M. S. Saleem, H. Yang, Edge version of topologi-cal degree based indices of Boron triangular nanotubes, Journal of Information and Optimization Sciences, 41(4), 2020, 973-990. https://doi.org/10.1080/02522667.2020.1743505
   Web of Science ®Google Scholar
• M. Cancan, M. Naeem, A.Q. Baig, W. Gao, A. Aslam, Vertex Szeged indices of P2n+FPn+1. Journal of Information and Optimization Sciences. 41(4), 2020, 991-1006. https://doi.org/10.1080/02522667.2020.1745381
   Web of Science ®Google Scholar
• M. Cancan, M. Naeem, A. Aslam, W. Gao, A.Q. Baig, Geometric arithmetic and Mostar indices of P2n+FPn+1, Journal of Information and Optimization Sciences, 41(4), 2020, 1007-1024. https://doi.org/10.1080/02522667.2020.1745382
   Web of Science ®Google Scholar
• M. Imran, M. Naeem, A.Q. Baig, Topological indices of polyhydroxybutyrate and poly-caprolactone, Journal of Information and Optimization Sciences, 41(4), 2020, 1025-1041. https://doi.org/10.1080/02522667.2020.1747192
   Web of Science ®Google Scholar