The convex and strictly convex on graphs
*Zainab Flaih HassanCorresponding authorZainab.flaih@ec.edu.iqDepartment of MathematicsMinistry of EducationOpen College of EducationNajaf, 54001, Iraq0000-0001-7254-6668View full profile → , Karrar Taher R. Aljamalykarrar.taher@ec.edu.iqDepartment of MathematicsMinistry of EducationOpen College of EducationNajaf, 54001, Iraq0000-0001-8447-3865View full profile →
* Corresponding author · click or hover a name for details
- Received:
- 06 Nov 2024
- Published Online:
- 12 Jun 2025
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JIM-2193
- Pages:
- 1643–1647
Abstract
Keywords
Subject Classifications
References
[1] L. Hőrmander, Notion of convexity, Birkhȁuser Bosten (1994).
[2] A. K. Abdulaali and H. B. Shelash, “The solvability degree of finite groups,” AIP conference proceedings (2023). [Online] Available: https://doi.org/10.1063/5.0113627.
[3] T. Oda, Convex Bodies and Algebraic Geometry: An Introduction to the Theory of Toric Varieties. Berlin, Germany: Springer-Verlag (1998).
[4] G. Ewald, Combinatorial Convexity and Algebraic Geometry, Springer-Verlag (1996).
[5] R. Dwilewicz, “An analytic point of view at toric varieties,” Serdica Math. J., vol. 33, pp. 163–240 (2007).
[6] C. Udrişte and T. Oprea, “H-convex Riemannian submanifolds,” Balkan J. Geom. Appl., vol. 13, no. 2, pp. 112–119 (2003).
[7] O. Bogaru, C. Udrişte, and C. S. Stamin, From curves to extrema, continuity and convexity, Proceeding of the 4th International Colloquium “Mathematics in Engineering and numerical physics”, BSG Proc., 14, Geom. Balkan Press, Bucharest, 58-62 (2007).
[8] O. Pogaru, C. Udrişte, and C. S. Stamin, Lateral extrema and convexity. Proc. of The International Conference “Differential Geometry-Dynamical Systems” DGDS-2007, Bucharest, Romania, BSG Proc. 15, Geometry Balkan Press, 82-88 (2007).
[9] C. U. Udrişte and V. Balan, “Differential operators and convexity on vector bundles endowed with (h, v)-metrics,” An. Ştiinţ. Univ. Al. I. Cuza Iaşi. Mat. (N.S.), vol. 43, no. 1, pp. 37–50 (1997).
[10] C. Udrişte, Convex functions and Optimization Methods on Reimannian Mani-folds, Mathematics and its Applications 297, Kluwer Academic Publishers Group, Dordrecht (1994).
[11] M. R. Pinheiro, “S-convexity—foundations for analysis,” Differ. Geom. Dyn. Syst., vol. 10, pp. 257–262, 2008.Z. Flaih and E. S. Bhaya, “A look at Sobolev spaces on graphs,” IOP Conf. Ser.: Mater. Sci. Eng., vol. 928, no. 4, Art. no. 042011 (2021).
[12] E. S. Bhaya and Z. Flaih, Sobolev Inequalities for Function on Graphs, Journal of Physis: Conferene Series, vol. 1804, pp. 012132 (2021).
[13] M. I. Ostrovskii, Sobolev spaces on graphs, Questions Mathematicae, vol. 28, no. 4, pp. 501-523 (2005).
[14] O. A. Hadi and H. B. Shelash, “Relation between cyclicity degree and cyclic graph of dihedral group D2n,” AIP conference proceedings, vol. 2834, pp. 090018-090018 (Jan. 2023). [Online] Available: https://doi.org/10.1063/5.0161568.
[15] S. Hussain, F. Afzal, D. Afzal, M. Cancan, S. Ediz, and M. R. Farahani, “Analyzing the boron triangular nanotube through topological indices via M-polynomial,” J. Discrete Math. Sci. Cryptography, vol. 24, no. 2, pp. 415-426, (2021). [Online] Available: https://doi.org/10.1080/09720529.2021.1882158.
[16] F. Afzal, S. Rukh, D. Afzal, M. R. Farahani, M. Cancan, and S. Ediz, “A study of non-commutative Von-Neumann regular rings,” J. Inf. Optim. Sci., vol. 42, no. 7, pp. 1425-1436 (2021). [Online] Available: https://doi.org/10.1080/02522667.2021.1896650.
[17] M. Nadeem, S. Ahmad, M. K. Siddiqui, M. A. Ali, M. R. Farahani, and A. J. M. Khalaf, “On some applications related with algebraic structures through different well known graphs,” J. Discrete Math. Sci. Cryptography, vol. 24, no. 2, pp. 451-471 (2021). [Online] Available: https://doi.org/10.1080/0972052.
[18] S. Ediz, M. Cancan, and M. R. Farahani, “Eccentric connectivity and connective eccentricity indices of generalized Petersen graphs,” Commun. Combinatorics Cryptogr. Comput. Sci., vol. 2021, no. 1, pp. 1-6 (2021).
[19] R. Ponraj, S. Prabhu, and M. Sivakumar, “Pair mean cordial labeling of total graph of some graphs and prism-related graphs,” Commun. Combinatorics Cryptogr. Comput. Sci., vol. 2024, no. 2, pp. 181-192 (2024).
[20] F. O. Oduol, and I. O. Okoth, “Counting vertices among all noncrossing trees by levels and degrees,” Commun. Combinatorics Cryptogr. Comput. Sci., vol. 2024, no. 2, pp. 193-212 (2024).
