On the Study Sum Graph of the Group Z_(p^n ) with Some Topological Index
DOI:
https://doi.org/10.29304/jqcm.2022.14.4.1122Keywords:
group sum graph, cyclic graph, order group, Euler graph, Hamilton graph, Zagreb index, Forgotten indexAbstract
In this research, we study the graph theory in the sum group via using concept of two distinct orders the sum it is always greatest that and equal the order of the group , where p is prime number. We have shown that the group sum graph of are connected, cyclic, etc. if it satisfied some properties of the graph theory and founded all the degree of graphs, we shall compute the famous of topological indices via generalized it.
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References
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[2] Alwardi, A., Alqesmah, A., Rangarajan, R., & Cangul, I. N. (2018). Entire Zagreb indices of graphs. Discrete mathematics, algorithms and applications, 10(03), 1850037.
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[8] Arif, N. E., Hasani, R., & Khalel, N. J. (2021, May). Pseudo-Von Neumann Regular Graph of Commutative Ring. In Journal of Physics: Conference Series (Vol. 1879, No. 3, p. 032012). IOP Publishing.
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[10] Khalel, N. J., & Arif, N. E. (2020). Chromatic number and some properties of Pseudo-Von Neumann regular graph of cartesian product of rings. Tikrit Journal of Pure Science, 25(3), 135-140.
[11] Anderson, D. F., Axtell, M. C., & Stickles, J. A. (2011). Zero-divisor graphs in commutative rings. Commutative Algebra, 23-45.
[12] Anderson, D. F., & Badawi, A. (2008). On the zero-divisor graph of a ring. Communications in Algebra, 36(8), 3073-3092.
[13] DeMeyer, F. R., McKenzie, T., & Schneider, K. (2002, July). The zero-divisor graph of a commutative semigroup. In Semigroup forum (Vol. 65, No. 2, pp. 206-214). Springer-Verlag.
[14] Milovanovic, I. Z., Ciric, V. M., Milentijevic, I. Z., & Milovanovic, E. I. (2017). On some spectral, vertex and edge degree–based graph invariants. MATCH Commun. Math. Comput. Chem, 77(1), 177-188.
[15] Matejić, M., Milovanović, I., & Milovanović, E. (2018). On bounds for harmonic topological index. Filomat, 32(1), 311-317.
[16] Jahanbani, A., Atapour, M., & Khoeilar, R. (2021). New Results on the Forgotten Topological Index and Coindex. Journal of Mathematics, 2021.
[17] Bharali, A., Doley, A., & Buragohain, J. (2020). Entire forgotten topological index of graphs. Proyecciones (Antofagasta), 39(4), 1019-1032.
[18] GÜRSOY, N. K. (2021). Computing the Forgotten Topological Index for Zero Divisor Graphs of MV-Algebras. Journal of the Institute of Science and Technology, 11(4), 3072-3085.
[19] Siu, M.-K. J. T. M. G. (1998). "Introduction to graph theory , by Robin J. Wilson. Pp. 171.£ 14.99. 1996. ISBN: 0-582-24993-7 (Longman)." 82(494): 343-344.
[20] Yaseen, M. T., & Ali, A. H. (2020). A new upper bound for the largest complete (k, n)-arc in PG (2, 71). In Journal of Physics: Conference Series (Vol. 1664, No. 1, p. 012045). IOP Publishing.
[2] Alwardi, A., Alqesmah, A., Rangarajan, R., & Cangul, I. N. (2018). Entire Zagreb indices of graphs. Discrete mathematics, algorithms and applications, 10(03), 1850037.
[3] Ranjini, P. S., Lokesha, V., & Usha, A. (2013). Relation between phenylene and hexagonal squeeze using harmonic index. Int. J. Graph Theory, 1(4), 116-121.
[4] Buragohain, J., Deka, B., & Bharali, A. (2020). A generalized ISI index of some chemical structures. Journal of molecular structure, 1208, 127843.
[5] Ahmed, M. S., Mohammed, A., & Arif, N. E. (2020). Hosoya Polynomial, Wiener Index, Coloring and Planar of Annihilator Graph of Zn. AL-Rafidain Journal of Computer Sciences and Mathematics, 14(2), 41-52.
[6] Nawaf, A. J., & Mohammad, A. S. (2021). Some Topological Indices and (Hosoya and Schultz) Polynomial of Subgroup intersection graph of a group Z_r. Journal of Al-Qadisiyah for computer science and mathematics, 13(1), Page-120.
[7] Nawaf, A. J., & Mohammad, A. S. (2021). Some Topological and Polynomial Indices (Hosoya and Schultz) for the Intersection Graph of the Subgroup of [Z] _ (r^ n). Ibn AL-Haitham Journal For Pure and Applied Sciences, 34(4), 68-77.
[8] Arif, N. E., Hasani, R., & Khalel, N. J. (2021, May). Pseudo-Von Neumann Regular Graph of Commutative Ring. In Journal of Physics: Conference Series (Vol. 1879, No. 3, p. 032012). IOP Publishing.
[9] Arif, N. E., & Khalel, N. J. (2020). Chromatic Number of Pseudo-Von neuman Regular Graph. Ibn AL-Haitham Journal For Pure and Applied Science, 33(2), 149-155.
[10] Khalel, N. J., & Arif, N. E. (2020). Chromatic number and some properties of Pseudo-Von Neumann regular graph of cartesian product of rings. Tikrit Journal of Pure Science, 25(3), 135-140.
[11] Anderson, D. F., Axtell, M. C., & Stickles, J. A. (2011). Zero-divisor graphs in commutative rings. Commutative Algebra, 23-45.
[12] Anderson, D. F., & Badawi, A. (2008). On the zero-divisor graph of a ring. Communications in Algebra, 36(8), 3073-3092.
[13] DeMeyer, F. R., McKenzie, T., & Schneider, K. (2002, July). The zero-divisor graph of a commutative semigroup. In Semigroup forum (Vol. 65, No. 2, pp. 206-214). Springer-Verlag.
[14] Milovanovic, I. Z., Ciric, V. M., Milentijevic, I. Z., & Milovanovic, E. I. (2017). On some spectral, vertex and edge degree–based graph invariants. MATCH Commun. Math. Comput. Chem, 77(1), 177-188.
[15] Matejić, M., Milovanović, I., & Milovanović, E. (2018). On bounds for harmonic topological index. Filomat, 32(1), 311-317.
[16] Jahanbani, A., Atapour, M., & Khoeilar, R. (2021). New Results on the Forgotten Topological Index and Coindex. Journal of Mathematics, 2021.
[17] Bharali, A., Doley, A., & Buragohain, J. (2020). Entire forgotten topological index of graphs. Proyecciones (Antofagasta), 39(4), 1019-1032.
[18] GÜRSOY, N. K. (2021). Computing the Forgotten Topological Index for Zero Divisor Graphs of MV-Algebras. Journal of the Institute of Science and Technology, 11(4), 3072-3085.
[19] Siu, M.-K. J. T. M. G. (1998). "Introduction to graph theory , by Robin J. Wilson. Pp. 171.£ 14.99. 1996. ISBN: 0-582-24993-7 (Longman)." 82(494): 343-344.
[20] Yaseen, M. T., & Ali, A. H. (2020). A new upper bound for the largest complete (k, n)-arc in PG (2, 71). In Journal of Physics: Conference Series (Vol. 1664, No. 1, p. 012045). IOP Publishing.
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Published
2022-12-31
How to Cite
Qasem, M. R., Arif, N. E., & Mohammed, A. S. (2022). On the Study Sum Graph of the Group Z_(p^n ) with Some Topological Index. Journal of Al-Qadisiyah for Computer Science and Mathematics, 14(4), Math Page 121–135. https://doi.org/10.29304/jqcm.2022.14.4.1122
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Math Articles
