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On some topological indices over rectangular grids | ||
| Journal of Hyperstructures | ||
| دوره 12، شماره 2، 2023، صفحه 322-335 اصل مقاله (323.9 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22098/jhs.2023.2806 | ||
| نویسندگان | ||
| Hadi Parsian* 1؛ Ali Parsian2 | ||
| 1Department of Civil Engineering, Faculty of Civil Engineering, Art and Architecture, WTIAU, Tehran, Iran. | ||
| 2Department of Mathematics, Tafresh University, Tafresh 39518 79611, Iran | ||
| چکیده | ||
| A topological index is a real number related to a graph,which is considered as a structural invariant. Some examples are Sombor index, Randi´c index, Zagreb indices, and Harmonic index.In the present paper, we consider the function Ind from the set of all rectangular grids to the set of real numbers, which assigns to each rectangular grid, one of its above indices. Then we show that the only non-degenerate indices over retangular grids, are Sombor index and Randi´c index, while Zagreb indices and the Harmonic index are degenerate. In the following, we determine rectangular grids with fixed diameter d, where maximum and minimum of the above indices occures on them, in the case m ≥ 3, n ≥ 3. Finally, we find the amounts of these indices. | ||
| کلیدواژه‌ها | ||
| Graph؛ Graphical indices؛ Isomorphism | ||
| مراجع | ||
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