ENERGI LAPLACE PADA KOMPLEMEN GRAF INVERS DARI GRUP DIHEDRAL

DWIKI, MARLINDA AGUSTINA (2018) ENERGI LAPLACE PADA KOMPLEMEN GRAF INVERS DARI GRUP DIHEDRAL. Other thesis, UNIVERSITAS ISLAM NEGERI MAULANA MALIK IBRAHIM MALANG.

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Abstract

Agustina, Dwiki Marlinda. 2018. Laplacian Energy of Complement Graph of Inverse Graph of Dihedral Group . Thesis. Department of Mathematics, Faculty of Science and Technology, Maulana Malik Ibrahim State Islamic Univer sity Malang. Advisor: (I) Dr. Abdussakir, M.Pd. (II) Mohammad Jamhuri, M.Si. Keyword : Laplacian energy, adjacency vertex matrix, degree matrix, Laplacian matrix, eigen value, invers graph, dihedral group The recent development of the graph theory is researching graph which formed from group. This thesis will examine the Laplacian energy of complement of invers graph of dihedral group. The method used in this thesis is library research using some references such as books and journals. Graph can be shown in matrix form, for example adjacency vertex matrix, degree matrix, and Laplacian matrix. These matrix can be used to find Eigen values. The sum of the absolute values of the Eigen values of a graph are called energy of and denoted by ( ) . The purpose of this research is to find a formula of Laplacian energy of complement of invers graph of dihedral group which will be used as a theorem. The result from this research are: Laplacian energy of co mplement of invers graph of dihedral group a. for is odd and is: ( ( ) ̅ ̅ ̅ ̅ ̅ ̅ ̅ ̅ ̅ ̅ ) | | b. for is even and ( ) , is: ( ( ) ̅ ̅ ̅ ̅ ̅ ̅ ̅ ̅ ̅ ̅ ) | | c . for is even and , is: ( ( ) ̅ ̅ ̅ ̅ ̅ ̅ ̅ ̅ ̅ ̅ ) | | with is the edge of complement of invers graph of dihedral group. For further research, it is suggested to continue the research about Laplacian energy from another groups

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