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.
|Number of pages||10|
|Journal||The Electronic Journal of Combinatorics: EJC|
|Publication status||Published - 19 Jul 2019|
Haemers, W. H., Sorgun, S., & Topcu, H. (2019). On the spectral characterization of mixed extensions of P-3. The Electronic Journal of Combinatorics: EJC, 26(3), [P3.16]. https://www.combinatorics.org/ojs/index.php/eljc/article/view/v26i3p16