| Authors | M. R. Oboudi, A. Z. Abdian, A. R. Ashrafi and L. W. Beineke |
|---|---|
| Journal | AKCE International Journal of Graphs and Combinatorics |
| Serial number | 1 |
| Volume number | 18 |
| Paper Type | Full Paper |
| Published At | 2021 |
| Journal Grade | ISI |
| Journal Type | Typographic |
| Journal Country | United Kingdom |
| Journal Index | Scopus, JCR |
Abstract
A graph G is said to be determined by the spectrum of its Laplacian matrix (DLS) if every graph with the same spectrum is isomorphic to G. In some recent papers it is proved that the friendship graphs and starlike trees are DLS. If a friendship graph and a starlike tree are joined by merging their vertices of degree greater than two, then the resulting graph is called a path-friendship graph. In this paper, it is proved that the path-friendship graphs, a natural generalization of friendship graphs and starlike trees, are also DLS. Consequently, using these results we provide a solution for an open problem.