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Advisor(s)
Abstract(s)
Let T be a tree with n≥2 vertices. Set S(T) for the set of all real symmetric matrices whose graph is T. Let A∈S(T)
and i∈{1,…,n} . We denote by A(i) the principal submatrix of A obtained after deleting the row and column i. We set mA(i)(0)=mA(0)+1, we say that i is a P-vertex of A. As usual, M(T) denotes the maximum nullity occurring of
B∈S(T). In this paper we determine an upper bound and a lower bound for the number of P-vertices in a matrix
A∈S(T)with nullity M(T). We also prove that if the integer b is between these two bounds, then there is a matrix E∈S(T) with b P-vertices and maximum nullity.
Description
Keywords
Trees Parter vertices Maximum nullity
Citation
Publisher
Elsevier