TARU PUBLICATIONS
Journal of Discrete Mathematical Sciences and Cryptography cover
Hybrid ·Peer-reviewed·ISSN (Online): 2169-0065·ISSN (Print): 0972-0529

Monthly Journal: Publishes theoretical and applied research in all areas of Discrete Mathematical Sciences, Cryptography, Combinatorics, Elliptic Curves and Information Security.

Issues up to 2022 co-published with and available at:Taylor & Francis Online
submissions@tarupublications.com
Open Access Research Article

Some parameters for the resize graph of G2(4)

* ,

* Corresponding author · click or hover a name for details

pp. 1375–1383Vol. 28Issue 4-BJune 2025DOI: 10.47974/JDMSC-2277 Crossmark XML
Received:
04 Feb 2025
Published Online:
26 Jun 2025
Article type:
Research Article
Language:
EN
Article no.:
JDMSC-2277
Pages:
1375–1383

Abstract

Topological indices provide important insights into the structural characteristics of molecular graphs. The present investigation proposes and explores a creative graph on a finite group G, which is known as the RIG. This graph is designated as ΓRSG2(4) indicating a simple undirected graph containing elements of G. Two distinct vertices are regarded as nearly the same if and only if their sum yields a non-trivial involution element in G. RIGs have been discovered in various finite groups. We examine several facets of the RIG by altering the graph through the conjugacy classes of G. Furthermore, we investigate the topological indices as applications in graph theory applying the distance matrix of the G2(4) group.

Keywords

Subject Classifications

05C9005C0920D0505C2505C69

References

[1] X. Li, S. Zhou, X. Ren, and X. Guo, “Structure and substructure connectivity of alternating group graphs,” Appl. Math. Comput., vol. 391, pp. 125639 (2021).
[2] P. K. Dixit, An Analysis of Group Theory: Advanced Topics and Applications, Modern Algebra, pp. 19.
[3] (http://brauer.maths.qmul.ac.uk/Atlas/v3/, (2021)] A. Oudah and A. Aubad, “Analysing the structure of A4-graphs for Mathieu groups,” J. Discrete Math. Sci. Cryptogr., vol. 24, no. 7, pp. 1907-1913 (2021).
[4] G. Araujo-Pardo and D. Leemans, “Edge-girth-regular graphs arising from biaffine planes and Suzuki groups,” Discrete Math., vol. 345, no. 10, pp. 112991 (2022).
[5] A. K. Mahato, R. Das, and S. K. Sahani, “Study on Application of Graph Theory in Artificial Intelligence (AI),” Quest: J. Geometry, Math. Quantum Phys., vol. 1, no. 3, pp. 1-8 (2024).
[6] A. T. Jawad and A. Aubad, “Studying the result involution graphs for HS and McL Leech lattice groups,” J. Interdiscip. Math., vol. 26, no. 5, pp. 829–834 (2023).
[7] A. Jund and H. Salih, “Result involution graphs of finite groups,” J. Zankoy Sulaimani, vol. 23, no. 1, pp. 113-118 (2021).
[8] A. Aubad and H. Salih, “More on Result Involution Graphs,” Iraqi J. Sci., vol. 64, no. 1, pp. 331-340 (2023).
[9] A. Hussain, M. Usman, and F. Zaman, “Lie group analysis, solitons, self-adjointness and conservation laws of the nonlinear elastic structural element equation,” J. Taibah Univ. Sci., vol. 18, no. 1, pp. 2294554 (2024).
[10] H. Hamdi, “Investigation of the order of elements 3 in certain twisted groups of Lie type,” Italian J. Pure Appl. Math., vol. 48, pp. 621–629 (2022).
[11] The GAP Group, “GAP Groups, Algorithms, and Programming,” Version 4.11.1, 18 Dec. (2022). [Online]. Available: http://www.gap-system.org.
[12] C. Cedillo, R. MacKinney-Romero, M. A. Pizaña, I. A. Robles, and R. Villarroel-Flores, “Yet Another Graph System, YAGS,” Version 0.0.5. [Online]. Available: http://xamanek.izt.uam.mx/yags/ (2019).
[13] R. Wilson, R. Abban, J. Bray, T. Breuer, C. Butler, R. Curtis, J. N. Bray, D. Holt, S. Linton, S. Norton, G. Hiss, K. Lux, A. Parker, and R. Parker, “A world wide web atlas of group representations,” [Online]. Available: http://brauer.maths.qmul.ac.uk/Atlas/v3/ (2021).
[14] Z. Du, A. Jahanbai, and S. M. Sheikholeslami, “Relationships between Randic index and other topological indices,” Commun. Combin. Optim., vol. 6, no. 1, pp. 137-154 (2021).
[15] M. N. Jauhari and F. Ali, “Survey on topological indices and graphs associated with a commutative ring,” in J. Phys.: Conf. Ser., vol. 1562, no. 1, pp. 012008 (June 2020).
[16] N. De, M. Cancan, M. Alaeiyan, and M. R. Farahani, “On some degree-based topological indices of mk-graph,” J. Discrete Math. Sci. Cryptogr., vol. 23, no. 6, pp. 1183-1194 (2020).
[17] J. B. Liu, S. N. Baig, I. A. Khan, F. Rauf, and M. A. Gondal, “Distance-based and bond additive topological indices of certain repurposed antiviral drug compounds tested for treating COVID-19,” Int. J. Quantum Chem., vol. 121, no. 10, p. e26617 (2021).
[18] G. H. Shirdel, H. Rezapour, and R. Nasiri, “Lower and upper bounds for Hyper-Zagreb index of graphs,” Iraqi J. Sci., vol. 61, no. 6, pp. 1401–1406 (2020).
[19] H. Ahmad, A. A. Almagrabi, R. A. Saeed, and M. M. A. Alobaidi, “Exploring the distance-based topological indices for total graphs via numerical comparison,” J. Math., vol. 2024, no. 1 (2024), doi: 10.1155/jom/4423113.
[20] X. Zhang, Q. Zheng, K. Ch. Das, J. Cao, and M. Imran, “On degree-based topological properties of two carbon nanotubes,” Polycycl. Aromat. Compd., vol. 42, no. 3, pp. 866–884 (2022). 
[21] A. H. Ahmed, A. Alwardi, and M. R. Salestina, “On domination topological indices of graphs,” Int. J. Analysis Appl., vol. 19, no. 1, pp. 47-64 (2021).
[22] I. Gutman, B. Furtula, and M. S. Oz, “Geometric approach to vertex-degree-based topological indices–Elliptic Sombor index, theory and application,” Int. J. Quantum Chem., vol. 124, no. 2, p. e27346 (2024).
[23] H. Ali, M. Shafiq, I. N. Mehmood, M. Imran, and S. N. Baig, “On the Degree-Based Topological Indices of Some Derived Networks,” Mathematics, vol. 7, no. 7, p. 612 (2019), doi: 10.3390/math7070612.
[24] J. L. Palacios, “More on Topological Indices and Their Reciprocals,” MATCH Commun. Math. Comput. Chem., vol. 92, pp. 55-63 (2024).
[25] A. Granados, S. Cabello, J. Rada, and J. A. Rodríguez-Velázquez, “New bounds for variable topological indices and applications,” J. Math. Chem., pp. 1-19 (2024).
[26] J. Kumar, R. P. Panda, and P. Parveen, “On the difference graph of power graphs of finite groups,” Quaestiones Mathematicae, vol. 47, no. 5, pp. 997-1018 (2024).
[27] J. M. Sigarreta, “Mathematical properties of variable topological indices,” Symmetry, vol. 13, no. 1, p. 43 (2020).

Views: 176Downloads: 56Citations: 0