## A Combinatorial Object

#### Hypercube graph

**Notation:** Q_n

**Vertices:** 2^n

**Edges:** 2^{n−1}n

**Diameter:** n

**Girth:** 4 if n ≥ 2

**Chromatic number:** 2

**Spectral Gap:** \frac{2}{n}

**Properties:**

Symmetric, Distance regular, Unit distance, Hamiltonian

Publications

**A. Davoodi (Joint with E. Gyori and A. Methuku), **

*An Erd\H{o}s-Gallai type theorem for uniform hypergraphs*

#### European J. Combin. 69(2018), 159-162

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**A. Mohammadian and B. Tayfeh-Rezaie, **

*Hadamard matrices with few distinct types*

#### Linear Multilinear Algebra (to appear)

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**M. R. Oboudi, **

*On the eigenvalues and spectral radius of starlike trees*

#### Aequat. Math. (2018), DOI: 10.1007/s00010-017-0533-4

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**A. Mohammadian and B. Tayfeh-Rezaie, **

*Star saturation number of random graphs*

#### Discrete Math. 341(2018), 1166-1170

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**H. Hajiabolhassan (Joint with M. Alishahi), **

*Chromatic number of random kneser hypergraphs*

#### J. Combin. Theory Ser. A (to appear)

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**M. R. Oboudi, **

*On the difference between the spectral radius and the maximum degree of graphs*

#### Algebra Discrete Math. (to appear)

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**G.R. Omidi and M. Shahsiah, **

*Diagonal Ramsey numbers of loose cycles in uniform hypergraphs*

#### SIAM J. Discrete Math. (to appear)

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**G. R. Omidi (Joint with L. Maherani), **

*Monochromatic Hamiltonian Berge-cycles in colored hypergraphs*

#### Discrete Math. (to appear)

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**A. Abdollahi (Joint with Sh. Janbaz and M. Ghahramani), **

*A large family of cospectral cayley graphs over dihedral groups*

#### Discrete Math. (to appear)

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**M. R. Oboudi, **

*Energy and Seidel energy of graphs*

#### MATCH Communications in Mathematical and in Computer Chemistry 75(2016), 291-303

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**M. R. Oboudi, **

*On the third largest eigenvalue of graphs*

#### Linear Algebra Appl. 503(2016), 164-179

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**M. R. Oboudi, **

*Cospectrality of complete bipartite graphs*

#### Linear Multilinear Algebra (2016), DOI: 10.1080/03081087.2016.1162133

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**M. R. Oboudi, **

*Bipartite graphs with at most six non-zero eigenvalues*

#### Ars Mathematica Contemporanea 11(2016), 315-325

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**A. Abdollahi and M. Jazaeri (Joint with E. R. van Dam), **

*Distance-regular graphs with least eigenvalue-2*

#### Des. Codes Cryptogr. (2016), DOI: 10.1007/s10623-016-0209-4

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**E. Ghorbani, **

*Proof of a conjecture on `plateaux' phenomenon of graph Laplacian eigenvalues*

#### Linear Algebra Appl. 506(2016), 274-278

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