REPRESENTASI GRUP DIHEDRAL DAN GRUP QUATERNION TERGENERALISASI PADA GRAF ORDER ELEMEN

Clarissa Elva Dheana, NIM.: 20106010019 (2024) REPRESENTASI GRUP DIHEDRAL DAN GRUP QUATERNION TERGENERALISASI PADA GRAF ORDER ELEMEN. Skripsi thesis, UIN SUNAN KALIJAGA YOGYAKARTA.

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Abstract

Order element graph is a representation of a finite group on a graph whose vertex is the element of the group and two distinct vertices e.g. g and h will be adjacent if the order of g divide the order of h or instead. Results of previous research related to the characterization of order element graph of cyclic group with order n = p, n = pk, and n = 2p include complete graph, tree graph, Euler graph, and Hamilton graph. This research focuses on the dihedral group D2n with n = p, n = 3k, and n = 2k and the generalized quaternion group Q4n with n = 2k and n = t, where p is a prime number, k is a positive integer, and t is an odd number. By generalizing the examples found by the author, the order element graph formed from the two groups are characterized. The resulting characterizations include complete graph, bipartite graph, planar graph, Eulerian graph, and Hamiltonian graph.

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