Indeks Eksentrisitas Zagreb Pertama dan Kedua Graf Koprima dari Grup Matriks Upper Unitriangular atas Ring Bilangan Bulat Modulo Prima

Muhammad Aris Abdillah, Dewi Ismiarti

Abstract


The coprime graph of a group G is a graph Γ_G with G is its set of vertices and any two distinct vertices are adjacent if and only if their order are relatively prime. Let p be a prime number, then G_p denotes the multiplicative group of 2×2 upper unitriangular matrices over ring of integers modulo p. The purposes of this research are to study the coprime graph Γ_(G_p ) and find the first and the second Zagreb eccentricity indices of Γ_(G_p ) for p≥3. The results of this research are as follows.
First Zagreb eccentricity index of coprime graph Γ_(G_p )is
E_1 (Γ_(G_p ))=4p-3.
Second Zagreb eccentricity index of coprime graph Γ_(G_p )is
E_2 (Γ_(G_p ))=2p-2.


Keywords


First Zagreb eccentricity index; Second Zagreb eccentricity index; Coprime graph; Upper unitriangular matrices

Full Text:

PDF

References


G. Chartrand, L. L. and Z. P., Graphs and Digraphs (Sixth Edition), Boca Raton: CRC Press, 2016.

J. A. Gallian, Contemporary Abstract Algebra 8th Edition, Boston: Brook/Cole Cengage Learning, 2012.

H. R. Dorbidi, "A Note On the Coprime Graph of A Group," International Journal of Group Theory, pp. 17-22, 2016.

A. S. Oliinyk and V. I. Sushchanskii, "Free Group of Infinite Unitriangular Matices," Mathematical Note, vol. 67, no. 03, pp. 320-324, 2000.

C. K. Gupta, B. S. Shetty dan V. Lokesha, “On The Graph of nilpotent matrix group of lenght one,” Discrete Mathematics, Algorithms and Applications, vol. 8, no. 01, pp. 1-31, 2016.




DOI: https://doi.org/10.18860/jrmm.v2i2.15668

Refbacks

  • There are currently no refbacks.