Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Self-dual polyhedra of given degree sequence   Given vertex valencies admissible for a self-dual polyhedral graph, we
describe an algorithm to explicitly construct such a polyhedron. Inputting in
the algorithm permutations of the degree sequence can give rise to
non-isomorphic graphs.
  As an application, we find as a function of $n\geq 3$ the minimal number of
vertices for a self-dual polyhedron with at least one vertex of degree $i$ for
each $3\leq i\leq n$, and construct such polyhedra. Moreover, we find a
construction for non-self-dual polyhedral graphs of minimal order with at least
one vertex of degree $i$ and at least one $i$-gonal face for each $3\leq i\leq
n$.

35
The categories of this paper are: mtrl-th
13
The categories of this paper are: quant-ph
0
The categories of this paper are: hep-ph
34
The categories of this paper are: chem-ph
12
The categories of this paper are: nucl-th
22
The categories of this paper are: chao-dyn
19
The categories of this paper are: eess
18
The categories of this paper are: econ
32
The categories of this paper are: atom-ph
21
The categories of this paper are: adap-org
25
The categories of this paper are: patt-sol
27
The categories of this paper are: comp-gas
7
The categories of this paper are: hep-th
3
The categories of this paper are: physics
10
The categories of this paper are: q-bio
17
The categories of this paper are: q-fin