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On the minimum number of distinct eigenvalues of athreshold graph
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NSTL
Elsevier
For a graph G, we associate a family of real symmetric matrices, S(G), where for any A is an element of S(G), the location of the nonzero off-diagonal entries of Aare governed by the adjacency structure of G. Let q(G) be the minimum number of distinct eigenvalues over all matrices in S(G). In this work, we give a characterization of all connected threshold graphs Gwith q(G) = 2. Moreover, we study the values of q( G) for connected threshold graphs with trace 2, 3, n - 2, n - 3, where nis the order of threshold graph. The values of q(G) are determined for all connected threshold graphs with 7 and 8 vertices with two exceptions. Finally, a sharp upper bound for q(G) over all connected threshold graph Gis given. (C) 2022 Elsevier Inc. All rights reserved.
Minimum number of distinct eigenvaluesThreshold graphsVertex-clique incidence matrixStrong spectral propertyEigenvalue of graphsMATRICESRANK
NSTL
Elsevier
