A graph is Laplacian integral if the spectrum of its Laplacian matrix consists entirely of integers. We consider the class of constructably Laplacian integral graphs -those graphs that be constructed from an empty graph by adding a sequence of edges in such a way that each time a new edge is added,
โฆ LIBER โฆ
Indecomposable laplacian integral graphs
โ Scribed by Robert Grone; Russell Merris
- Publisher
- Elsevier Science
- Year
- 2008
- Tongue
- English
- Weight
- 189 KB
- Volume
- 428
- Category
- Article
- ISSN
- 0024-3795
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## Abstract Let __G__ be a simple graph of order __n__ with Laplacian spectrum {ฮป~__n__~, ฮป~__n__โ1~, โฆ, ฮป~1~} where 0=ฮป~__n__~โคฮป~__n__โ1~โคโ โคฮป~1~. If there exists a graph whose Laplacian spectrum is __S__={0, 1, โฆ, __n__โ1}, then we say that __S__ is Laplacian realizable. In 6, Fallat et al. posed