Total edge irregularity strength of subdivision of star

Abstract

This This research is the development from Siddique's research on edge irregularity strength of subdivision of star. Siddiqui [3] had determined the total edge irregularity strength of subdivision of star S_n^m for 1 <= m <= m and n >= 3. However, the total edge of irregularity strength for star subdivision S_n^m for m >= 9 and n >= 3 are still in an open problem and also the total edge irregularity strength of subdivision of star by inserting m_i vertices on different to every edge of a star S_n yet to be determined. In this paper, it will be proven that the total edge irregularity strength of subdivision of star S_n^m for m >= 9 and n >= 3 and the total edge irregularity strength of subdivision of star S_n^{m_1, m_2, ...m_s} for m_i >= 1, m_i < m_{i+1}, 1 <= i <= n, and n >= 3.

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