Total coloring for splitting graph of certain graphs

A total coloring of a graph G is an assignment of colors to all the vertices and edges of the
graph for which no two adjacent or incident vertices and edges receives the same color. The total
chromatic number of G, denoted by
'' (
) G  , is the minimum number of colors suffice for a total
coloring. Behzad and Vizing was introduced the total coloring conjecture independently and
claims that,
''
( ) 1 ( ) ( ) 2 G G G        . In this paper, we determined total coloring conjecture
for ( ), ( ),
n n
S L S S ( ), ( ),
n n
S H S T ( ), ( )
n n
S TL S SL respectively.