Domatic Number in Cartesian Graph
Journal Title: International Journal of Engineering Sciences & Research Technology - Year 30, Vol 3, Issue 4
Abstract
A domatic partition of a graph GH = (V, E) is a partition of V into disjoint sets V1,V2, …Vk such that each Vj is a dominating set for GH. The maximum number of dominating sets, which the vertex set of a Cartesian graph GH can be partitioned is called the domatic number of a graph GH. It is denoted by dom(GH) or d(GH). In this paper, we discuss the sharp bounds for dom(GH) and all Cartesian graphs attaining these bounds are characterized. We also describe the Cartesian product on complete graph G and H of order m and n and derive some properties and bounds on it.
Authors and Affiliations
A. Sasireka*1
Keywords
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