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- W4289362080 abstract "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 $P_3$." @default.
- W4289362080 created "2022-08-02" @default.
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- W4289362080 date "2018-10-30" @default.
- W4289362080 modified "2023-09-23" @default.
- W4289362080 title "On the spectral characterization of mixed extensions of $P_3$" @default.
- W4289362080 doi "https://doi.org/10.48550/arxiv.1810.12615" @default.
- W4289362080 hasPublicationYear "2018" @default.
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