2 research outputs found
Set Representations of Linegraphs
Let be a graph with vertex set and edge set . A family
of nonempty sets is a set representation of
if there exists a one-to-one correspondence between the vertices in and the sets in such that if and only if S_i\cap S_j\neq \es. A set representation
is a distinct (respectively, antichain, uniform and simple) set representation
if any two sets and in have the property (respectively, , and ). Let . Two set
representations and are isomorphic if
can be obtained from by a bijection from
to . Let denote a class of set
representations of a graph . The type of is the number of equivalence
classes under the isomorphism relation. In this paper, we investigate types of
set representations for linegraphs. We determine the types for the following
categories of set representations: simple-distinct, simple-antichain,
simple-uniform and simple-distinct-uniform