Journal of Pure and Applied Mathematics: Advances and ApplicationsAuthor's: A. R. Latheeshkumar and Anil Kumar V.
Pages: [97] - [108]
Received Date: November 23, 2016
Submitted by:
DOI: http://dx.doi.org/10.18642/jpamaa_7100121741
A hypergraph is an ordered pair 
where V is a finite nonempty set
called vertices and E is a collection of subsets of V,
called hyper edges or simply edges. A subset T of vertices in a
hypergraph H is called a vertex cover if T has a
nonempty intersection with every edge of H. The vertex covering
number 
of H is the minimum size of a
vertex cover in H. Let 
be the family of vertex covering sets of
H with cardinality i and let 
be the cardinality of 
The polynomial 
is defined as vertex cover polynomial of
H. For a graph 
denotes the hypergraph with vertex set
V and edge set 
In this paper, we prove that the total
domination polynomial of a connected graph G is the vertex
cover polynomial of 
Using this result, we determine total
domination polynomials of cartesian products of certain classes of
graphs.
total domination, vertex cover, total domination polynomial.
