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bibo:abstract "The power graph is a graph that represents the power relation between elements\r\nwithin a group, where two distinct vertices are connected by an edge if one\r\nelement is a power of the other. This study focuses on determining the spectrum of\r\nthe power graph over the dihedral group D2n restricted to the orders n = pk and\r\nn = pq, where p and q are distinct prime numbers and k is a natural number. In\r\nthe computation, the process begins by constructing the power graph of the dihedral\r\ngroup D2n based on the power relations among its elements. Once the graph structure\r\nand the degree of each vertex are identified, the power graph is represented in\r\nthe form of an adjacency matrix, Laplacian matrix, signless Laplacian matrix, as\r\nwell as the normalized forms of these three representation matrices. From each representation\r\nmatrix, the characteristic polynomial equation is constructed to find the\r\neigenvalues along with their multiplicities, collectively referred to as the spectrum\r\nof the graph. During the matrix simplification and the computation of eigenvalues,\r\nidentifying the element orders and generating subgroups becomes highly crucial. In\r\nthe case of n = pk, the subgroups form an ordered chain, allowing for the systematic\r\ncalculation of vertex degrees and the determination of eigenvalues. Conversely,\r\nin the case of n = pq, the subgroup structure exhibits branching, leading to high\r\ncomplexity in calculating the vertex degrees. Consequently, the determination of\r\nthe spectrum for the n = pq case is specifically limited to the adjacency matrix.\r\nThe results of this research formulate the characteristic polynomials along with the\r\neigenvalues of the corresponding graph representation matrices for each case of the\r\npower graph on the dihedral group."^^xsd:string;
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skos:prefLabel "515.6 Metode Analitik - Matematika" .
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dc:title "HTML Summary of #76839 \n\nSPEKTRUM GRAF PANGKAT ATAS GRUP DIHEDRAL\n\n";
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foaf:name "UIN SUNAN KALIJAGA YOGYAKARTA"^^xsd:string;
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foaf:name "FAKULTAS SAINS DAN TEKNOLOGI, UIN SUNAN KALIJAGA YOGYAKARTA"^^xsd:string;
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foaf:familyName "Ahmad Ikhlasul A’mal"^^xsd:string;
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foaf:name "NIM.: 22106010025 Ahmad Ikhlasul A’mal"^^xsd:string;
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