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https://www.um.edu.mt/library/oar/handle/123456789/109154| Title: | The two classes of singular line graphs of trees |
| Authors: | Sciriha, Irene |
| Keywords: | Graph theory -- Mathematics Polynomials -- Mathematical models Bipartite graphs Eigenvalues -- Data processing Laplacian matrices |
| Issue Date: | 1999 |
| Publisher: | Universita degli Studi di Messina |
| Citation: | Sciriha, I. (1999). The two classes of singular line graphs of trees. In 5th Workshop on Combinatorics. Rendiconti del Seminario Matematico Messina, 5(21)(II), 167-180. |
| Abstract: | A graph G is singular if its adjacency matrix A(G) is singular. We consider the multiplicity of the eigenvalue 0 for line graphs LG and show that it is at most one for LT where T is a tree. Moreover, if LT is singular, then T is shown to be even. Furthermore, the Polynomial Reconstruction Conjecture, a variant of Ulam 's Reconstruction Conjecture, is shown to be true for singular line graphs of trees. The analysis gives rise to a partition of singular line graphs of trees into two classes. |
| URI: | https://www.um.edu.mt/library/oar/handle/123456789/109154 |
| Appears in Collections: | Scholarly Works - FacSciMat |
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| File | Description | Size | Format | |
|---|---|---|---|---|
| The two classes of singular line graphs of trees 1999.pdf Restricted Access | 335.77 kB | Adobe PDF | View/Open Request a copy |
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