1Dept. of Mathematics, Government Arts College (Autonomous), Karur -639005. Email: drduk80@rediffmail.com
2Research Scholar, Distance Education, Department of Mathematics, Gandhigram Rural University, Gandhigram. Dindigul -634002. Email: sasireka07@yahoo.co.in
Online published on 22 February, 2013.
A subset S of vertices of a Cartesian graph GoH is called a global connected dominating set if S is both a global dominating set and a connected dominating set. The global connected domination number is the minimum cardinality of a global connected dominating set of GoH and is denoted by Ygc(GoH). In this paper, sharp bounds for Ygc(GoH) are supplied and all Cartesian graphs attaining these bounds are characterized. We also characterize the Cartesian product on complete graph G and H of order mxn with Ygc =n where 2:5n:5m. m is the order of G and n is the order of H.
Global connected dominating set (GCD-set), global connected domination number, global dominating set (GD-set), connected dominating set (CD-set), Non-split dominating set (NSD-set)
