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Some Bicyclic Graphs Having 2 as Their Laplacian Eigenvalues.
- Source :
-
Mathematics (2227-7390) . Dec2019, Vol. 7 Issue 12, p1233. 1p. - Publication Year :
- 2019
-
Abstract
- If G is a graph, its Laplacian is the difference between the diagonal matrix of its vertex degrees and its adjacency matrix. A one-edge connection of two graphs G 1 and G 2 is a graph G = G 1 ⊙ u v G 2 with V (G) = V (G 1) ∪ V (G 2) and E (G) = E (G 1) ∪ E (G 2) ∪ { e = u v } where u ∈ V (G 1) and v ∈ V (G 2) . In this paper, we study some structural conditions ensuring the presence of 2 in the Laplacian spectrum of bicyclic graphs of type G 1 ⊙ u v G 2 . We also provide a condition under which a bicyclic graph with a perfect matching has a Laplacian eigenvalue 2. Moreover, we characterize the broken sun graphs and the one-edge connection of two broken sun graphs by their Laplacian eigenvalue 2. [ABSTRACT FROM AUTHOR]
- Subjects :
- *EIGENVALUES
Subjects
Details
- Language :
- English
- ISSN :
- 22277390
- Volume :
- 7
- Issue :
- 12
- Database :
- Academic Search Index
- Journal :
- Mathematics (2227-7390)
- Publication Type :
- Academic Journal
- Accession number :
- 140954533
- Full Text :
- https://doi.org/10.3390/math7121233