A Positive Combinatorial Formula for the Complexity of the q-Analog of the n-Cube
نویسنده
چکیده
The number of spanning trees of a graph G is called the complexity of G and denoted c(G). A classical result in algebraic graph theory explicitly diagonalizes the Laplacian of the n-cube C(n) and yields, using the Matrix-Tree theorem, an explicit formula for c(C(n)). In this paper we explicitly block diagonalize the Laplacian of the q-analog Cq(n) of C(n) and use this, along with the Matrix-Tree theorem, to give a positive combinatorial formula for c(Cq(n)). We also explain how setting q = 1 in the formula for c(Cq(n)) recovers the formula for c(C(n)).
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عنوان ژورنال:
- Electr. J. Comb.
دوره 19 شماره
صفحات -
تاریخ انتشار 2012