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6 votes
3 answers
251 views

How many $40$-vertex cubic bipartite graphs have determinant $\pm 3$?

To get some feel for the size of a particular computation, I would like to know the approximate number of (pairwise-nonisomorphic) cubic bipartite graphs on $40$ vertices whose bipartite adjacency ...
Gordon Royle's user avatar
  • 12.7k
2 votes
0 answers
267 views

On the determinant of incidence matrices (of graphs and other geometries)

Let $\Gamma = (P,L,I)$ be a point-line geometry (here, $P$ is the point set, $L$ the line set, and $I$ is the symmetric incidence relation). (As an example, $\Gamma$ could be a graph.) I suppose $\...
THC's user avatar
  • 4,547
0 votes
1 answer
204 views

Are these particular kinds of matrices well known?

Given two positive integers $n$ and $a \leq \frac{n}{2}$ consider a $n \times n$ matrix $A$ such that, all the diagonal entries are either $a$ or $a+1$ all the non-zero off-diagonal entries are $\pm ...
user6818's user avatar
  • 1,893
4 votes
0 answers
657 views

determinant of fibonacci-sum graphs

We have a simple graph with vertices $\{v_1, v_2, ... v_n\}$. The adjacency matrix of this graph is $A= (a_{ij})$ so that $a_{ij}=1$ if $i+j$ belongs to the Fibonacci sequence; $a_{ij}=0$ ...
zoha's user avatar
  • 41