ISI(G) Topological Index of Sum Graphs For Some Finite Groups: ISI(G) Topological Index of Sum Graphs For Some Finite Groups

mahera rabee

doi:10.24237/ASJ.01.03.743C

Authors

mahera rabee Department of Mathematics, College of Education for pure Science, University of Tikrit.

DOI:

https://doi.org/10.24237/ASJ.01.03.743C

Keywords:

generalized ISI index, topological index, degree, cyclic graph, connected graph.

Abstract

A topological index can capture much information about a mathematical structure into an actual number. The topological indices have an essential role in theoretical mathematics. A topological index is a graphـbased

Recently, unified approaches have been adopted to study these topological

indices in groups. In this work, we look at the generalized ISI index since we can obtain some other topological indices as exceptional cases of sum graphs of groups. These generalized indices reduce the work for calculating some topological indexes differently.

References

References:

West, D. B. (2008). Introduction to graph theory, 2nd ed. (Vol. 2). Upper Saddle River: Prentice hall.

Alwardi, A., Alqesmah, A., Rangarajan, R., & Cangul, I. N. (2018). Entire Zagreb indices of graphs. Discrete mathematics, algorithms, and applications, 10(03), 1850037.

Ranjini, P. S., Lokesha, V., & Usha, A. (2013). Relation between phenylene and hexagonal squeeze using a harmonic index. Int. J. Graph Theory, 1(4), 116-121.

Buragohain, J., Deka, B., & Bharali, A. (2020). A generalized ISI index of some chemical structures. Journal of molecular structure, 1208, 127843.

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.

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.

Nawaf, A. J., & Mohammad, A. S. (2021). Some Topological and Polynomial Indices (Hosoya and Schultz) for the Intersection Graph of the Subgroup of [1] _ (r^ n). Ibn AL-Haitham Journal For Pure and Applied Sciences, 34(4), 68-77.

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.

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.

Khalel, N. J., & Arif, N. E. (2020). Chromatic number and some properties of Pseudo-Von Neumann regular graph of the cartesian product of rings. Tikrit Journal of Pure Science, 25(3), 135-140.

Anderson, D. F., Axtell, M. C., & Stickles, J. A. (2011). Zero-divisor graphs in commutative rings. Commutative Algebra, 23-45.

Anderson, D. F., & Badawi, A. (2008). On the zero-divisor graph of a ring. Communications in Algebra, 36(8), 3073-3092.

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.

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.

Matejić, M., Milovanović, I., & Milovanović, E. (2018). On bounds for harmonic topological index. Filomat, 32(1), 311-317.

Jahanbani, A., Atapour, M., & Khoeilar, R. (2021). New Results on the Forgotten Topological Index and Coindex. Journal of Mathematics, 2021.

Bharali, A., Doley, A., & Buragohain, J. (2020). Entire forgotten topological index of graphs. Proyecciones (Antofagasta), 39(4), 1019-1032.

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.

Mahera R. Q., Nabeel E. A., Akram S. M. (2022). On the Study Sum Graph of the Group Z_(p^n ) With Some Topological Index. Journal of Al-Qadisiyah for Computer Sciences and Mathematics.

Mahera R. Q., Akram S. M. &Nabeel E. A. (2023). New Concept of Finite Group〖( Z〗_(p^n q)) on the Sum Graph with Some Topological Index. Preprint.

Mahera R. Qasem, Nabeel E. Arif & Akram S. Mohammed. (2023).Sum Graph of Z_(p^n q^m ) Groups and some Topological Indices of G+ (Z_(p^n q^m )). Preprint.

Mansour, I. A., Qasem, M. R., Salih, M. A., & Hussain, M. Q. (2021). Characterization of semi-hollow-lifting module. Materials Today: Proceedings.‏

Qasem, M. R., Salih, M. A., & Noori, S. M. (2020). Soft set and its direct effect on a ring structure. Journal of Intelligent & Fuzzy Systems, 38(3), 2885-2888.‏

Qasem, M. R., Salih, M. A., & Arif, G. E. (2019). Modern cyclic groups and their relation with classical groups: Theory and Application. Opción, 35(88), 1379-1388.‏

MaheraRabee Qasem, Unitary and commutative rings and their relations with ideals. Materials Today: Proceedings

Rasha A Isewid, Nabila I Aziz, Samer R Yaseen & Mahera Rabee Qasem(2020).

Some Properties of Regular and Normal Space on Topological Graph Space. Published under license by IOP Publishing Ltd.

Mahera R. Q., Akram S. M. &Nabeel E. A. (2023). Some General Topological Indices of Finite Group (Zp qm) on the Sum Graph. Preprint.

ISI(G) Topological Index of Sum Graphs For Some Finite Groups