Abstract: For any graph semi total block graph whose set of vertices is the union
of the set of vertices and blocks of G in which two vertices are adjacent if and only if the
corresponding vertices of G are
adjacent or the corresponding members are incident. Let F be a minimum edge dominating set of G. If E-F
contains an edge dominating set then is called a complementary edge
dominating set of G with respect to
F. The complementary edge domination
number of G
is the minimum number of edges in a complementary edge dominating set of G.
A complementary edge dominating set of a graph H is called a complementary edge semi total block
dominating set of G. A complementary
edge semi total block domination number of G
is the
minimum cardinality of a complementary edge semi total block dominating set of G.
In this paper, many bounds on are obtained in terms of members of G
but not the members of H. In addition,
we establish the relationship of this concept with other domination parameters.
Also, Nordhaus-Gaddum type results are obtained.
Keywords and phrases: complementary edge semi total block domination number, edge domination number, complementary edge domination number.
