Geodesic
A \(q\)-analogue of Graham, Hoffman and Hosoya's theorem
The electronic journal of combinatorics, Tome 17 (2010)
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Graham, Hoffman and Hosoya gave a very nice formula about the determinant of the distance matrix $D_G$ of a graph $G$ in terms of the distance matrix of its blocks. We generalize this result to a $q$-analogue of $D_G$. Our generalization yields results about the equality of the determinant of the mod-2 (and in general mod-$k$) distance matrix (i.e. each entry of the distance matrix is taken modulo 2 or $k$) of some graphs. The mod-2 case can be interpreted as a determinant equality result for the adjacency matrix of some graphs.
DOI : 10.37236/470
Classification : 05A30, 05C12
Mots-clés : determinant, distance matrix, q-analogue 
@article{10_37236_470,
     author = {Sivaramakrishnan Sivasubramanian},
     title = {A \(q\)-analogue of {Graham,} {Hoffman} and {Hosoya's} theorem},
     journal = {The electronic journal of combinatorics},
     year = {2010},
     volume = {17},
     doi = {10.37236/470},
     zbl = {1188.05027},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/470/}
}
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Sivaramakrishnan Sivasubramanian. A \(q\)-analogue of Graham, Hoffman and Hosoya's theorem. The electronic journal of combinatorics, Tome 17 (2010). doi: 10.37236/470

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