The term "flower graph" is used for several different families of graphs.
The name could also be used for the parity-dependent family of unit-distance graphs produced by a single geometric construction
for every 
.
The construction arranges claw graphs and joins their
noncentral vertices along three paths,
two of which are interchanged at each step. In the notation of Fouquet et al.
(2010), these are the twisted Isaacs graphs 
for odd 
and 
for even 
.
The first parameter 
in 
is the number of graph
cycles induced after the central vertex of each
claw graph is deleted. For odd 
, the closing permutation
is a transposition of the three paths
and has two permutation cycles, so 
. For even 
, the closing permutation is
the identity permutation and has three one-element
permutation cycles, so 
. The graphs 
for odd 
are the flower snarks.
Herbster and Pontil (2006) define a flower graph as a graph obtained by connecting the first vertex of a path
graph with 
vertices to the root vertex
of an 
-ary
tree of depth one. The vertices
of this graph can be indexed so that vertices
1 to 
correspond to "stem vertices" and vertices 
to 
to "petals."
Seoud and Youssef (2017) define a flower graph as the graph obtained from a helm graph by joining each pendent vertex to the central vertex (Gallian 2018).
