On the Spectrum of Threshold Graphs
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The antiregular connected graph on r vertices is defined as the connected graph whose vertex degrees take the values of r−1 distinct positive integers. We explore the spectrum of its adjacency matrix and show common properties with those of connected threshold graphs, having an equitable partition with a minimal number r of parts. Structural and combinatorial properties can be deduced for related classes of graphs and in particular for the minimal configurations in the class of singular graphs.
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2020 ◽
Vol 39
(6)
◽
pp. 1627-1647
2019 ◽
Vol 55
(2)
◽
pp. 169-175
Keyword(s):
Keyword(s):