University of Mohaghegh Ardabili Journal of Hyperstructures 2251-8436 15 1 2026 06 01 Normalized distance Laplacian energy change due to edge deletion in complete graph and complete multipartite graph 49 64 4645 10.22098/jhs.2025.18132.1124 EN Indulal Gopal Mathematics, St Aloysious College, Edathua Jinu Mary SB College Chganganachery Journal Article 2025 08 19 Let G be a connected graph with a distance matrix D. The eigenvalues of D forms the distance spectrum or D−spectrum<br />of G. The transmission of a vertex v in G is the sum of the distances from v to all other vertices of G and T (G) is the diagonal matrix with transmission of the vertices as diagonal entries. The distance Laplacian matrix is defined as D^L(G)=T(G)−D(G) and the normalized distance Laplacian matrix as D^L(G)=T (G)^−1/2D^L(G)T (G)^−1/2. The normalized-distance Laplacian energy is defined as D^LE(G)=∑_i=1ⁿ |ρ_i^L−1|. Let D^LE(G − e) be the normalized Laplacian energy of distance when an edge e is removed. In this paper we are studying the Normalized Distance Laplacian<br />energy change due to an edge deletion. https://jhs.uma.ac.ir/article_4645_979a3ae8df36b5533bcd677d757ef73e.pdf