Moreover, we proved that each partial limit of this sequence is achievable on a certain subsequence of any sequence satisfying condition (20), in particular on certain subsequence of any

arithmetic sequence (Theorem 8).

An (a,d)-edge-antimagic total labeling ((a,d)-EAT for short) of G is the total labeling with the property that the edge-weights form an

arithmetic sequence starting from a and having common difference d, where a greater than 0 and d [greater than or equal to] 0 are two given integers.

Summary: TEHRAN (FNA)- A group of researchers at the Iranian University of Kashan successfully discovered the geometrical pattern governing the structures of fullerenes and carbon nanotubes and formulated the number of carbon atoms constituting fullerenes/CNTs as

arithmetic sequences.

This metonymy makes no mention of the essential characteristic, the mapping between geometric and

arithmetic sequences.

An additional benefit of the recursive formula in this instance is that it reinforces the essence of an

arithmetic sequence as one in which the same amount is added to each term to attain the next term.

Solak, On the circulant matrices with

arithmetic sequence, International Journal of Contemporary Matematical Sciences, 5(2010), No.

A bijective mapping (Equation) is called an (Equation) -edge-antimagic vertex labeling, if the set of edge-weights (Equation) forms an

arithmetic sequence with the intial term (Equation) and the difference (Equation), where (Equation) is a positive and is a nonnegative integer.