| Autor: |
Haemers, Willem H., Sorgun, Sezer, Topcu, Hatice |
| Rok vydání: |
2018 |
| Předmět: |
|
| Druh dokumentu: |
Working Paper |
| Popis: |
A mixed extension of a graph $G$ is a graph $H$ obtained from $G$ by replacing each vertex of $G$ by a clique or a coclique, whilst two vertices in $H$ corresponding to distinct vertices $x$ and $y$ of $G$ are adjacent whenever $x$ and $y$ are adjacent in $G$. If $G$ is the path $P_3$, then $H$ has at most three adjacency eigenvalues unequal to $0$ and $-1$. Recently, the first author classified the graphs with the mentioned eigenvalue property. Using this classification we investigate mixed extension of $P_3$ on being determined by the adjacency spectrum. We present several cospectral families, and with the help of a computer we find all graphs on at most $25$ vertices that are cospectral with a mixed extension of $P_3$. |
| Databáze: |
arXiv |
| Externí odkaz: |
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