Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: ON $(\triangle, 1)$-GRAPHS   Let $G = (V, E)$ be a graph and $\lambda $ a non-negative integer. A graph
$G$ is called a $(\lambda, 1)$-{\em graph} if $ (c0)$ $G$ is neither a complete
graph no an edge-empty graph, $ (c1)$ every edge in $G$ belongs to exactly
$\lambda$ triangles, and $(c2)$ every two non-adjacent vertices in $G$ are the
end-vertices of exactly one two-edge path in $G$. It turns out that there are
infinitely many feasible 4-tuples $(v, d, \lambda, 1)$ with $\lambda \ge 1$. On
the other hand (and this is our main result), there is no $(v, d, \lambda,
1)$-graphs with $\lambda \ge 1$. As a byproduct, we obtain a generalization of
the classical Friendship Theorem.

33
The categories of this paper are: plasm-ph
12
The categories of this paper are: nucl-th
14
The categories of this paper are: math-ph
30
The categories of this paper are: q-alg
16
The categories of this paper are: stat
3
The categories of this paper are: physics
6
The categories of this paper are: astro-ph
34
The categories of this paper are: chem-ph
1
The categories of this paper are: cs
27
The categories of this paper are: comp-gas
28
The categories of this paper are: alg-geom
35
The categories of this paper are: mtrl-th
20
The categories of this paper are: acc-phys
13
The categories of this paper are: quant-ph
26
The categories of this paper are: bayes-an
25
The categories of this paper are: patt-sol