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Rahimi, Mehdi, Assari, Amir. (1404). A family of graphs generated by Hilbert space. سامانه مدیریت نشریات علمی, 6(1), 114-124. doi: 10.22098/jfga.2025.16516.1146
Mehdi Rahimi; Amir Assari. "A family of graphs generated by Hilbert space". سامانه مدیریت نشریات علمی, 6, 1, 1404, 114-124. doi: 10.22098/jfga.2025.16516.1146
Rahimi, Mehdi, Assari, Amir. (1404). 'A family of graphs generated by Hilbert space', سامانه مدیریت نشریات علمی, 6(1), pp. 114-124. doi: 10.22098/jfga.2025.16516.1146
Rahimi, Mehdi, Assari, Amir. A family of graphs generated by Hilbert space. سامانه مدیریت نشریات علمی, 1404; 6(1): 114-124. doi: 10.22098/jfga.2025.16516.1146

A family of graphs generated by Hilbert space

Journal of Finsler Geometry and its Applications
دوره 6، شماره 1، 2025، صفحه 114-124    اصل مقاله (311.63 K)
نوع مقاله: Original Article
شناسه دیجیتال (DOI): 10.22098/jfga.2025.16516.1146
نویسندگان
Mehdi Rahimi* 1؛ Amir Assari2
1Department of Mathematics, Faculty of Science, University of Qom, Qom, Iran
2School of Computing, Engineering & Digital Technologies, Tesside University, Middlesbrough, United Kingdom
چکیده
In this paper, we introduce a novel class of graphs based on Hilbert spaces, termed Hilbert graphs. Constructed using the inner product defined on a Hilbert space, Hilbert graphs leverage the concept of orthogonality, where orthogonal elements correspond to adjacent vertices. We demonstrate that Hilbert graphs are regular and vertex transitive, with the clique number equal to the dimension of the corresponding Hilbert space. Our investigation encompasses various properties of Hilbert graphs, including connectivity, girth, diameter, and chromatic number, and we draw comparisons with Cayley graphs and zero divisor graphs.
کلیدواژه‌ها
Hilbert Graph؛ orthogonality؛ regular graph؛ vertex transitive graph
مراجع
  1. M. Afkhami, K. Khashyarmanesh and K.Nafar, Generalized Cayley graphs associated to commutative rings, Linear Algebra Appl. 437(3) (2012), 1040{1049.
2. R. Akhtar, T. Jackson-Henderson, R. Karpman, M. Boggess, I. Jim´enez, A. Kinzel, D.Pritikin, On the unitary Cayley graph of a finite ring, Electron. J. Combin. 16(1) (2009),Research Paper 117, 13 pp.
3. D. F. Anderson, M. C. Axtell, J. A. Stickles, Zero-divisor graphs in commutative rings,Commutative algebra, Noetherian and non-Noetherian perspectives, 23{45, Springer,New York, 2011.
4. R. Aravamudhan and B. Rajendran, On antipodal graphs, Discrete Mathematics. 49(1984), 193-195.
5. A. Assari and F. Sheikhmiri, Normal edge-transitive Cayley graphs of the group U6n,Int. J. Comb. 2014, Art. ID 628214, 4 pp.
6. A. Assari, N. Hosseinzadeh, and D. Macpherson, Set-homogeneous hypergraphs, Journal of the London Mathematical Society, 108(5) (2023), pp.1852-1885.
7. A. Assari, H. Kasiri, and A. R. Alehafttan, GRAPHS induced by vector spaces, Palestine Journal of Mathematics, 12(3) (2023), 216-223.
8. A. Assari, and M. Rahimi, Graphs generated by measures, Journal of Mathematics,2016(1), ID:1706812, Doi.org/10.1155/2016/1706812.
9. A. Assari, and M. Rahimi, On Beck’s Coloring for Measurable Functions, Iranian Journal of Mathematical Sciences and Informatics, 16(2) (2021), 1-10.
10. I. Beck, Colouring of commutative rings, J. Algebra. 116(1) (1988), 208-226.
11. A. Badawi, On the Dot Product Graph of a Commutative Ring, Communications in Algebra. 43(2015), 43-50.
12. A. Badawi, On the annihilator graph of a commutative ring, Comm. Algebra. 42(1)(2014), 108-121.
13. A. Badawi, On the total graph of a ring and its related graphs: a survey, Commutative algebra, 39{54, Springer, New York, 2014.
14. A. Cayley, Desiderata and Suggestions: No. 2. The Theory of Groups: Graphical Representation. Amer. J. Math. 1(2) (1878), 174-176.
15. J. B. Conway, A Course in Functional Analysis, Springer-Verlag, 1994.
16. M. R. Darafsheh, A. Assari, Normal edge-transitive Cayley graphs on non-abelian groups of order 4p, where p is a prime number, Sci. China Math. 56(1) (2013), 213-219.
17. C. Ir`ene; O. Hudry, A. Lobstein, Minimizing the size of an identifying or locatingdominating code in a graph is NP-hard, Theoret. Comput. Sci. 290(3) (2003), 2109-2120.
18. X. G. Fang, C. H. Li, M. Y. Xu, On edge-transitive Cayley graphs of valency four,European J. Combin. 25(7) (2004), 1107-1116.
19. C. Godsil, On the full automorphism group of a graph, Combinatorica. 1(3) (1981),243-256.
20. C. Godsil, G. Royle, Algebraic graph theory, Graduate Texts in Mathematics, 207.Springer-Verlag, New York, 2001. xx+439 pp.
21. R. Halaˇ s, M. Jukl, On Beck’s colouring of posets, Discrete Math. 309(13) (2009), 4584-4589.
22. B. L. Hartnell, D.F. Rall, On dominating the Cartesian product of a graph and K2,Discuss. Math. Graph Theory. 24(3) (2004), 389{402.
23. S. K. Nimbhorkar, M. P. Wasadikhar, L. Demeyer, Colouring of meet-semilattices, Ars Combin. 84 (2007) 97-104.
24. C. ER. Praeger, Finite normal edge-transitive Cayley graphs, Bull. Austral. Math. Soc.60(2) (1999), 207-220.
25. P. J. Slater, Dominating and reference sets in a graph, J. Math. Phys. Sci. 22(4) (1988),445-455.
26. D. H. Smith, Primitive and imprimitive graphs, Q. J. Math. 22 (1971), 551-557.
27. D. R. Wood, An algorithm for finding a maximum clique in a graph, Oper. Res. Lett.21(5) (1997), 211{217. 

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