Title of article :
On Vertex Covering Transversal Domination Number of Regular Graphs
Author/Authors :
Vasanthi, R Department of Mathematics - Alagappa Chettiar College of Engineering and Technology - Karaikudi - Tamil Nadu 630 004 - India , Subramanian, K Department of Mathematics - Alagappa Government Arts College - Karaikudi - Tamil Nadu 630 003 - India
Abstract :
A simple graph 𝐺 = (𝑉, 𝐸) is said to be 𝑟-regular if each vertex of 𝐺 is of degree 𝑟. The vertex covering transversal domination number 𝛾vct(𝐺) is the minimum cardinality among all vertex covering transversal dominating sets of 𝐺. In this paper, we analyse this parameter on different kinds of regular graphs especially for 𝑄𝑛 and 𝐻3,𝑛. Also we provide an upper bound for 𝛾vct of a connected cubic graph of order 𝑛≥8. Then we try to provide a more stronger relationship between 𝛾 and 𝛾vct.
Keywords :
Vertex Covering Transversal , Regular Graphs , simple graph
Journal title :
The Scientific World Journal
