Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Kocay's lemma, Whitney's theorem, and some polynomial invariant
  reconstruction problems   Given a graph G, an incidence matrix N(G) is defined for the set of distinct
isomorphism types of induced subgraphs of G. If Ulam's conjecture is true, then
every graph invariant must be reconstructible from this matrix, even when the
graphs indexing the rows and the columns of N(G) are unspecified. It is proved
that the characteristic polynomial, the rank polynomial, and the number of
spanning trees of a graph are reconstructible from its N-matrix. These results
are stronger than the original results of Tutte in the sense that actual
subgraphs are not used. It is also proved that the characteristic polynomial of
a graph with minimum degree 1 can be computed from the characteristic
polynomials of all its induced proper subgraphs. The ideas in Kocay's lemma
play a crucial role in most proofs. Here Kocay's lemma is used to prove
Whitney's subgraph expansion theorem in a simple manner. The reconstructibility
of the characteristic polynomial is then demonstrated as a direct consequence
of Whitney's theorem as formulated here.

15
The categories of this paper are: nucl-ex
14
The categories of this paper are: math-ph
6
The categories of this paper are: astro-ph
30
The categories of this paper are: q-alg
23
The categories of this paper are: solv-int
8
The categories of this paper are: hep-ex
9
The categories of this paper are: nlin
12
The categories of this paper are: nucl-th
17
The categories of this paper are: q-fin
11
The categories of this paper are: hep-lat
32
The categories of this paper are: atom-ph
19
The categories of this paper are: eess
37
The categories of this paper are: supr-con
24
The categories of this paper are: dg-ga
22
The categories of this paper are: chao-dyn
16
The categories of this paper are: stat