Prof. Dr. Hailiza Kamarulhaili2025-08-122025-08-12https://dspace.academy.edu.ly/handle/123456789/1715Tambahan pula, semua tenaga yang dipertimbangkan dibandingkan untuk membuat kesimpulan bahawa tenaga graf memberikan nilai nombor genap manakala nisbah tenaga graf (nisbah antara tenaga Laplacian dan tenaga campuran graf bagi jam pasir bercampur) adalah ganjil. Jumlah tenaga graf Laplacian dan tenaga graf campuran bagi jam pasir bercampur ialah dua kali ganda hasil tambahHourglass matrix is a square matrix obtained from quadrant interlocking factorization, known as 𝑊𝐻 factorization, which can be represented in mixed graph. Recent establishment of hourglass matrix and its factorization technique does not show the all the properties of the matrix. In this thesis, properties of 𝑊𝐻 factorization were put forward which include its existence for every strict dominant diagonal matrix, that its 𝐻𝑠𝑦𝑠𝑡𝑒𝑚 forms a lower triangular invertible matrix and its counterpart 𝑊-matrix forms an upper triangular invertible matrix.APPLICATION IN GRAPHENERGIES