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Independence Saturation and Extended Domination Chain in Graphs

2007; Elsevier BV; Linguagem: Inglês

10.1080/09728600.2007.12088831

2543-3474

S. Arumugam, M. Subramanian, Anand Nagar,

Graph theory and applications

The six basic parameters relating to domination, independence and irredundance satisfy a chain of inequalities given by ir ≤ γ ≤ i ≤ β0 ≤ Γ ≤ IR where ir, IR are the irredundance and upper irredundance numbers, γ,Γ are the domination and upper domination numbers and i, β0 are the independent domination number and independence number respectively. In this paper, we introduce the concept of independence saturation number IS of a graph which extends the above domination chain. We also consider the edge-analogue of this extended domination chain.