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Sattar, Tayyiba; Sardar, Muhammad Shoaib; Alaeiyan, Mehdi; Farahani, Moahmmad Reza; Cancan, Murat; Tas, Ziyattin

The study of the \(b\)-chromatic number of some classes of fractal graphs. (The study of the \(b\)-choromatic number of some classes of fractal graphs.) (English) Zbl 1496.05057

J. Discrete Math. Sci. Cryptography 25, No. 5, 1509-1524 (2022).

MSC:

05C15 Coloring of graphs and hypergraphs
05C75 Structural characterization of families of graphs
05C76 Graph operations (line graphs, products, etc.)

Keywords:

\(b\)-coloring; \(b\)-chromatic number; Sierpinski graph; Sierpinski gasket network; house graph
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Full Text: DOI

References:

[1] Wilson, R.J.. Introduction to Graph Theory, John Wiley and Sons, Inc.605 Third Ave. New York, NYUnited States,1986. https://dl.acm.org/doi/
[2] Bollobas, B., Modern graph theory, volume 184 of Graduate Texts in Mathematics (1998), Springer-Verlag · Zbl 0902.05016 · doi:10.1007/978-1-4612-0619-4
[3] Tosuni, B., Graph Coloring Problems in Modern Computer Science, European Journal of Interdis-ciplinary Studies, 1, 2, 87-95 (2015) · doi:10.26417/ejis.v1i2.p87-95
[4] Barrus, M. D.; Hartke, S. G.; Kumbhat, M., Graph Classes Characterized Both by For-bidden Subgraphs and Degree Sequences, Journal of Graph Theory, 57, 2, 131-148 (2005) · Zbl 1139.05054 · doi:10.5555/1330411.1330414
[5] Corteela, S.; Valencia-PabonbJuan, M.; Verac, C., On approximating the b-chromatic number, Discrete Applied Mathematics, 146, 1, 106-110 (2005) · Zbl 1057.05032 · doi:10.1016/j.dam.2004.09.006
[6] Vijayalakshmi, D.; Thilagavathi, K.; Roopesh, N., The b-chromatic number of M[Cn], M[Pn], M[Fn] and M[Wn], Open journal of Discrete Mathematics, 1, 2, 85 (2011) · Zbl 1370.05072 · doi:10.4236/ojdm.2011.12010
[7] Irving, R. W.; Manlove, David F., The b-chromatic number of a graph, Discrete Applied Mathematics, 91, 1-3, 127-141 (1999) · Zbl 0933.05051 · doi:10.1016/S0166-218X(98)00146-2
[8] Jakovac, M.; Klavzar, S., The b-chromatic number of cubic graphs, Graphs and Combinatories, 26 · Zbl 1221.05145 · doi:10.1007/s00373-010-0898-9
[9] Vivin, V., The b-chromatic number of corona graphs, Utilitas Mathematica, 88, 299-307 (2012) · Zbl 1256.05079
[10] Scorer, R. S.; Grundy, P. M.; Smith, C. A. B., Some binary games, Math. Gaz, 28, 96-103 (1944) · doi:10.2307/3606393
[11] Kouider, M.; Maheo, M., Some bounds for the b-chromatic number of a graph, Discrete Mathematics, 256, 1-2, 267-277 (2002) · Zbl 1008.05056 · doi:10.1016/S0012-365X(01)00469-1
[12] Nagarathinam, R.; Parvathi, N., On b-coloring line, middle and total graph of tadpole graph, In AIP Conference Proceedings, 1 (2020) · doi:10.1063/5.0026012
[13] Vaidya, S. K.; Isaac, Rakhimol V., The b-chromatic number of some path related graphs, International Journal of Mathematics and Scientific Computing, 4, 1, 7-12 (2014) · Zbl 1371.05098
[14] Vernold Vivin, J.; Vekatachalamb, M., On b-chromatic number of sun let graph and wheel graph families, Journal of the Egyptian Mathematical Society, 23, 2, 215-218 · Zbl 1327.05126 · doi:10.1016/j.joems.2014.05.011
[15] Skums, P., Graph fractal dimension and the structure of fractal networks, Journal of Complex Networks, 8, 4, 037 (2020) · Zbl 1481.90099 · doi:10.1093/comnet/cnaa037
[16] Jiang, Z.; Yan, W., Some Two-Point Resistances of the Sierpinski Gasket Network, J Stat Phys, 172, 824-832 (2018) · Zbl 1396.05031 · doi:10.1007/s10955-018-2067-0
[17] Nizami, A. R.; Shabbir, K.; Sardar, M. S.; Qasim, M.; Cancan, M.; Ediz, S., Base polynomials for degree and distance based topological invariants of n-bilinear straight pentachain, Journal of Information and Optimization Sciences, 8 (2021) · doi:10.1080/02522667.2021.1903202
[18] Sardar, M. S.; Alaeiyan, M.; Farahani, M. R.; Cancan, M.; Ediz, S., Resistance distance in some classes of rooted product graphs obtained by Laplacian generalized inverse method, Journal of Information and Optimization Sciences, 42, 7, 1447-1467 (2021) · doi:10.1080/02522667.2021.1899210
[19] Ahmad, Z.; Chaudhary, M. A.; Baig, A. Q.; Zahid, M. A., On metric dimension of P(n; 2)K_1 graph, Journal of Discrete Mathematical Sciences and Cryptography, 24, 2, 629-645 (2021) · Zbl 1483.05051 · doi:10.1080/09720529.2021.1907017
[20] Ahmad, Z.; Chaudhary, M. A.; Baig, A. Q.r; Zahid, M. A., Fault-tolerant metric dimension of P(n; 2) K_1 graph, Journal of Discrete Mathematical Sciences and Cryptography, 24, 2, 647-656 (2021) · Zbl 1483.05052 · doi:10.1080/09720529.2021.1899209
[21] Sajjad, W.; Shoaib Sardar, M.; Cancan, M.; Ediz, S.; Baig, A. Q., On modified eccentric connectiv-ity index of nanotube, Journal of Information and Optimization Sciences, 41, 4, 959-972 (2020) · doi:10.1080/02522667.2020.1745380
[22] Sardar, M. S.; Xu, S.-A.; Sajjad, W.; Zafar, S.; Cangul, I. N.; Farahani, M. R., An explicit formula for the harmonic indices and harmonic polynomials of carbon nanocones CNC k [n], Journal of Information and Optimization Sciences, 41, 4, 879-890 (2020) · doi:10.1080/02522667.2020.1753304
[23] Amer, A.; Naeem, M.; Rehman, H. Ur; Irfan, M.; Saleem, M. S.; Yang, H., Edge version of topologi-cal degree based indices of Boron triangular nanotubes, Journal of Information and Optimization Sciences, 41, 4, 973-990 (2020) · doi:10.1080/02522667.2020.1743505
[24] Cancan, M.; Naeem, M.; Baig, A. Q.; Gao, W.; Aslam, A., Vertex Szeged indices of P_2n+FP_n+1, Journal of Information and Optimization Sciences, 41, 4, 991-1006 (2020) · doi:10.1080/02522667.2020.1745381
[25] Cancan, M.; Naeem, M.; Aslam, A.; Gao, W.; Baig, A. Q., Geometric arithmetic and Mostar indices of P_2n+FP_n+1, Journal of Information and Optimization Sciences, 41, 4, 1007-1024 (2020) · doi:10.1080/02522667.2020.1745382
[26] Imran, M.; Naeem, M.; Baig, A. Q., Topological indices of polyhydroxybutyrate and poly-caprolactone, Journal of Information and Optimization Sciences, 41, 4, 1025-1041 (2020) · doi:10.1080/02522667.2020.1747192
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