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Moreover, the minimum (resp. maximum) number of edges for all (connected) graphs with pendent vertices and nullity η are determined, and the extremal graphs are characterized..
arbitrary pendent vertex of the star) is the unique tree that maximizes the distance spectral radius, and conjecture the structure of a tree which minimizes the distance
This work is Project 10671026 supported by National Natural Science Foundation of China, Postdoctoral Scientific Research Foundation of Heilongjiang Province (no. HB200801165) and
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In [19], the Perron-Frobenius property stands for having the spectral radius as a positive eigenvalue with a nonnegative eigenvector; this is also the definition used in
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[r]
In this note, we generalize the explicit formulae in [5] for the polar factors of nonsingular real square matrices of order 2, and obtain explicit formulae for polar factors of n − by
