Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the convexity number of the complementary prism of a tree   A set of vertices $S$ of a graph $G$ is a (geodesic)convex set, if $S$
contains all the vertices belonging to any shortest path connecting between two
vertices of $S$. The cardinality of maximum proper convex set of $G$ is called
the convexity number, con$(G)$ of $G$. The complementary prism $G\bar{G}$ of
$G$ is obtained from the disjoint union of $G$ and its complement $\bar{G}$ by
adding the edges of a perfect matching between them. In this work, we examine
the convex sets of the complementary prism of a tree and derive formulas for
the convexity numbers of the complementary prisms of all trees.

28
The categories of this paper are: alg-geom
23
The categories of this paper are: solv-int
3
The categories of this paper are: physics
30
The categories of this paper are: q-alg
14
The categories of this paper are: math-ph
29
The categories of this paper are: funct-an
37
The categories of this paper are: supr-con
36
The categories of this paper are: cmp-lg
26
The categories of this paper are: bayes-an
25
The categories of this paper are: patt-sol
31
The categories of this paper are: ao-sci
20
The categories of this paper are: acc-phys
8
The categories of this paper are: hep-ex
24
The categories of this paper are: dg-ga
5
The categories of this paper are: gr-qc
17
The categories of this paper are: q-fin