Chromaticity of Sylow Graph for the Cyclic Groups
DOI:
https://doi.org/10.31642/JoKMC/2018/120208Keywords:
Chromatic number; , Chromatic polynomial; , Chromaticity;, Sylow Graph.Abstract
In our work, we will find the new results on the chromatic uniqueness of Sylow graphs of cyclic group , . Moreover, we will determine the results about the chromatic number and chromatic polynomial of these graphs. We will discuss all the cases of , where is the prime number. Moreover, we prove that if , , and , then is not , where and , otherwise it is .
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] H. Al-Janabi, G. Bacsó, Integral-root Polynomials and Chromatic Uniqueness of Graphs. Journal of Discrete Mathematical Sciences and Cryptography, 24(4), 1127-1147 (2021). DOI: https://doi.org/10.1080/09720529.2021.1891697
[2] H. Al-Janabi, G. Bacso´, Chromatic Uniqueness of Zero-Divisor Graphs. The Art of Discrete and Applied Mathematics, 6(1),(2022). DOI: https://doi.org/10.26493/2590-9770.1544.f34
[3] I. Beck, Coloring of commutative rings. J. Algebra 116, 208-226, (1988). DOI: https://doi.org/10.1016/0021-8693(88)90202-5
[4] G. D. Birkhoff, A determinate formula for the number of ways of coloring a map. Annal. Math, 14, no. 2, 42-46, (1912). DOI: https://doi.org/10.2307/1967597
[5] W. C. Calhoun, Counting the subgroups of some finite groups. Amer. Math. Monthly 941,54–59, (1987). DOI: https://doi.org/10.1080/00029890.1987.12000593
[6] S. R. Cavior, The subgroups of the dihedral groups, Math. Mag. 48 (1975). DOI: https://doi.org/10.1080/0025570X.1975.11976454
[7] C. Y. Chao and E.G. Whitehead Jr., On chromatic equivalence of graphs. Theory and applications of graphs (Proc. Internet Con£., Western Mich. Univ., Kalamazoo, Mich., 1976), pp. 121-131. Lecture Notes in Math., Vol. 642, Springer, Berlin, 1978. J. Shaanxi Normal Univ. 20, 75-79, (1992). DOI: https://doi.org/10.1007/BFb0070369
[8] G. Chartrand and P. Zhang, Chromatic graph theory. Taylor and Francis Group, LLC. USA (2009). DOI: https://doi.org/10.1201/9781584888017
[9] G.L. Chia, A bibliography on ChPs. Discrete Math. 172, 175-191, (1997). DOI: https://doi.org/10.1016/S0012-365X(97)90031-5
[10] G.L. Chia, On graphs unique l colorable under the action of their automorphism.
[11] F. M. Dong, K. M. Koh and K. L. Teo, ChPs and chromaticity of graphs, World Scientific Publishing Co. Pte. Ltd. Singapore (2005).
[12] S. Sh. Gehet, A. M. Khalaf, ChPs and Chromaticity of Zero-Divisor Graphs. 3rd International Conference on Applied Mathematics and Pharmaceutical Sciences, April, Singapore, (2013).
[13] O. A. Hadi, H. B. Shelash, Finite Groups with the Probability of Parameters. Accepted for publication in the IOP Journal of Physics, 2th international conferences IICPS, Babelon University, Iraq, submit 2021.
[14] O. A. Hadi, H. B. Shelash, Relation between Normality degree and Normal Graph of Some of Finite Groups. 1th Annual Iranian International Group Theory Conference IGTC, (2022).
[15] O. A. Hadi, H. B. Shelash, Relation between Sylow degree and Sylow graph. Iranian Algebra Seminar Persian Gulf University, Bushehr, Iran, (2022).
[16] O. A. Hadi, H. B. Shelash, Sylow degree and Sylow graph of C_n and D_2n. Proceeding Book in 1th international conferences on engineering and applied Natural Sciences ICEANS, Konya, Turkey, (2022).
[17] O. A. Hadi, H. B. Shelash, Relation between Cyclicity degree and cyclic graph of Dihedral group D_2n. Accepted for publication in the AIP Journal of Physics,4th international Scientific Conference of Engineering Sciences and Advances Technologies IICESAT, (2022). DOI: https://doi.org/10.1063/5.0161568
[18] K.M. Koh and K.L. Teo, The search for chromatically unique graphs-II. Discrete Math. 172,59-78, (1997). DOI: https://doi.org/10.1016/S0012-365X(96)00269-5
[19] K.M. Koh and K.L. Teo, The search for chromatically unique graphs. Graphs and Combin. 6, no. 3, 259-285, (1990). DOI: https://doi.org/10.1007/BF01787578
[20] L. Lov´asz, Combinatorial Problems and Exercises. AMS Chelsea Publishing, 2nd edition, American Mathematical Society, Island (1993).
[21] R. C. Read, An introduction to ChPs. J. Combin. Theory 4, (1968). DOI: https://doi.org/10.1016/S0021-9800(68)80087-0
[22] S. Roman, Fundamentals of Group Theory. 52-71, (2011). DOI: https://doi.org/10.1007/978-0-8176-8301-6
[23] H. Whitney, The coloring of graphs. Ann. Math. 33, 688-718, (1932). DOI: https://doi.org/10.2307/1968214
[24] A. A. Zykov, On Some Properties of Linear Complexes. Matematicheskii Sbornik, 24(66), 163-188 (1949).
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