A function
f
with domain and range are respectively the edge set of graph
G
and natural number up to
, and a function
f
with domain and range are respectively the vertex set of graph
G
and the even natural number up to
2
are called a total
k
-labeling where
2
. The total
k
-labeling of graph
G
by the condition that every two different edges have different weight is called an edge irregular reflexive
k
-labeling, where for any edge
, the weight is
. The reflexive edge strength of the graph
G
, denoted by
is the minimum
k
for graph
G
which has an edge irregular reflexive
k
-labelling. In this study, we obtained the
of graphs which their vertex degrees show an almost regularity properties.