INDEKS-INDEKS KONEKTIVITAS DARI GRAF KOPRIMA DARI GRUP QUATERNION TERGENERALISASI

Aulia Tiffani Rizky, NIM.: 20106010027 (2024) INDEKS-INDEKS KONEKTIVITAS DARI GRAF KOPRIMA DARI GRUP QUATERNION TERGENERALISASI. Skripsi thesis, UIN SUNAN KALIJAGA YOGYAKARTA.

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Abstract

The generalized quaternion group is an extension of the quaternion group of order 8 denoted by Q4n. While the coprime graph is a graph formed from the representation of a finite group on a graph where vertices are elements in the group with edges connecting the two elements in the group if and only if their orders are mutually prime, the coprime graph is denoted by ΩG. This research studies the form and properties of coprime graphs over Q4n with n is an odd prime number, n = 2k, and n = 2p, and find its connectivity indices. The research method used is a literature study, starting with substituting the value of n in Q4n, then the form and properties of the coprime graph over Q4n are obtained, and continued by finding 6 indices connectivity. Previously, the form and properties of the coprime graph over the generalized quaternion group with n is an odd prime number, namely the tripartite graph, and n = 2k is a star graph, and the 6 connectivity indices was obtained, followed by another coprime graph with n = 2p is the tripartite graph. The result in this study is the connectivity indices on coprime graphs of the form n = 2p by raising a special case in the formation of coprime graphs. Furthermore, six connectivity indices are obtained, namely First Zagreb Index, Second Zagreb Index, Wiener Index, hyper-Wiener Index, Harary Index, and Harary Index.

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