An integral graph, not to be confused with an integral embedding of a graph, is defined as a graph whose graph spectrum consists entirely of integers. The notion was first introduced by Harary and Schwenk (1974). The numbers of simple integral graphs on
, 2, … nodes are 0, 2, 3, 6, 10, 20, 33, 71, … (OEIS A077027), illustrated above for small
Đang xem: Integral graph
The numbers of connected simple integral graphs on
, 2, … nodes are 1, 1, 1, 2, 3, 6, 7, 22, 24, 83, … (OEIS A064731), illustrated above for small
The following table lists common graph classes and the their members which are integral.
of the form
|cycle graph||2, 3, 4, 6|
|prism graph||3, 4, 6|
The following table lists some special named graphs that are integral and gives their spectra.
|small triakis octahedral graph|
|truncated tetrahedral graph|
Harary, F. and Schwenk, A.J. “Which Graphs have Integral Spectra?” In Graphs and Combinatorics (Ed. R.Bari and F. Harary). Berlin: Springer-Verlag, pp.45-51, 1974.
Sloane, N.J.A. Sequences 064731 A and A077027 in “The On-Line Encyclopedia of Integer Sequences.”
CITE THIS AS:
Weisstein, Eric W. “Integral Graph.” Fromwnyrails.org–A wnyrails.org Web Resource. https://wnyrails.org/IntegralGraph.html
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