### Abstract

Original language | English |
---|---|

Article number | P3.16 |

Number of pages | 10 |

Journal | The Electronic Journal of Combinatorics: EJC |

Volume | 26 |

Issue number | 3 |

Publication status | Published - 19 Jul 2019 |

### Cite this

*The Electronic Journal of Combinatorics: EJC*,

*26*(3), [P3.16].

}

*The Electronic Journal of Combinatorics: EJC*, vol. 26, no. 3, P3.16.

**On the spectral characterization of mixed extensions of P-3.** / Haemers, Willem H.; Sorgun, Sezer; Topcu, Hatice.

Research output: Contribution to journal › Article › Scientific › peer-review

TY - JOUR

T1 - On the spectral characterization of mixed extensions of P-3

AU - Haemers, Willem H.

AU - Sorgun, Sezer

AU - Topcu, Hatice

PY - 2019/7/19

Y1 - 2019/7/19

N2 - 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.

AB - 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.

M3 - Article

VL - 26

JO - The Electronic Journal of Combinatorics: EJC

JF - The Electronic Journal of Combinatorics: EJC

SN - 1097-1440

IS - 3

M1 - P3.16

ER -