On some topological indices over rectangular grids
محل انتشار: مجله ابرساختارها، دوره: 12، شماره: 2
سال انتشار: 1402
نوع سند: مقاله ژورنالی
زبان: انگلیسی
مشاهده: 47
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شناسه ملی سند علمی:
JR_JHSMS-12-2_008
تاریخ نمایه سازی: 16 بهمن 1402
چکیده مقاله:
A topological index is a real number related to a graph, which is considered as a structural invariant. Some examples are Sombor index, Randic 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 Randic index, while Zagreb indices and the Harmonic index are degenerate. In the following, we determine rectangular grids with xed diameter d, where maximum and minimum of the above indices occures on them, in the case m ۳; n ۳. Finally, we nd the amounts of these indices.
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نویسندگان
Hadi Parsian
Department of Civil Engineering, Faculty of Civil Engineering, Art and Architecture, WTIAU, Tehran, Iran.
Ali Parsian
Department of Mathematics, Tafresh University, Tafresh ۳۹۵۱۸ ۷۹۶۱۱, Iran