SOME NOTES ON THE LAPLACIAN ENERGY OF EXTENDED ADJACENCY MATRIX
نویسندگان
چکیده
منابع مشابه
Some results on the energy of the minimum dominating distance signless Laplacian matrix assigned to graphs
Let G be a simple connected graph. The transmission of any vertex v of a graph G is defined as the sum of distances of a vertex v from all other vertices in a graph G. Then the distance signless Laplacian matrix of G is defined as D^{Q}(G)=D(G)+Tr(G), where D(G) denotes the distance matrix of graphs and Tr(G) is the diagonal matrix of vertex transmissions of G. For a given minimum dominating se...
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Proof. We first recall that every non-singular matrix B can be written B = QR, where Q is an orthonormal matrix Q and R is upper-triangular matrix R with positive diagonals1 We will use a slight variation of this fact, writing B = RQ. Now, since QT = Q−1, QAQT has exactly the same eigenvalues as A. Let Rt be the matrix t ∗R+ (1− t)I, and consider the family of matrices Mt = RtQAQR t , as t goes...
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ژورنال
عنوان ژورنال: Journal of Science and Arts
سال: 2020
ISSN: 2068-3049,1844-9581
DOI: 10.46939/j.sci.arts-20.3-a01