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All Journal JURNAL MATEMATIKA STATISTIKA DAN KOMPUTASI International Journal of Computing Science and Applied Mathematics-IJCSAM
Arif Munandar
UIN Sunan Kalijaga Yogayakarta
Mathematics

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Connectivity of Power Graphs of Cyclic Groups with Specific Orders Riyanto; Arif Munandar
(IJCSAM) International Journal of Computing Science and Applied Mathematics Vol. 12 No. 2 (2026)
Publisher : LPPM Institut Teknologi Sepuluh Nopember

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.12962/j24775401.ijcsam.v12i2.9603

Abstract

The power graph is defined as a graph whose vertexset consists of the elements of a group, where two vertices arejoined by an edge if one element is a power of the other. In thisresearch we discuss the power graph of a cyclic group of order n=pq, with p and q distinct prime numbers, illustrates theconnectivity among its vertices and reveals important topologicalproperties such as the diameter and the clique number. Fur-thermore, this study also examines the degrees of the verticesand provides an analysis of the Hamiltonian, Eulerian, andplanar characteristics of the graph. These findings highlighthow algebraic structures can be effectively explored throughgraph-theoretical perspectives, offering deeper insights into theinterplay between group theory and graph topology.
Connectivity of Non-Coprime Graph over Dihedral Group Winda Cahya Dwi Wahyuni; Arif Munandar
Jurnal Matematika, Statistika dan Komputasi Vol. 23 No. 1 (2026): September 2026
Publisher : Department of Mathematics, Hasanuddin University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20956/y76mg453

Abstract

Let Γ be the non-coprime graph of the dihedral group of order 2n. This research investigates the connectivity properties of Γ, particularly its Eulerian, semi-Eulerian, Hamiltonian, and planar properties. The research begins by examining several properties related to the dihedral group, and then identifying the connectivity patterns that are formed in the non-coprime graph through the analysis of the order of elements in the group. These patterns then serve as the basis for determining its connectivity properties. The results show that Γ is Eulerian when n = 2k, where k ≥ 2, and semi-Eulerian if and only if n = 2p, where p is an odd prime. Furthermore, the graph is Hamiltonian for n = 2k or n = 2p, where p is an odd prime. In addition, the graph is planar if and only if n = 2 or n = 3. These results indicate that the factorization form of n strongly influences the connectivity structure and graph properties of the non-coprime graph over the dihedral group.
Co-Authors Riyanto Winda Cahya Dwi Wahyuni