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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، مهر 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
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