Changing and Unchanging 2-Rainbow Independent Domination

Domination number is of practical interest in several theoretical and applied scenes. In the problem of wireless networking, the dominating idea is used to deduce an efficient route within the ad-hoc mobilenetworks. It has also been used for the summarization of documents and making a design of secure web-systems for electrical recursive grids. In this paper, we explore an important class of domination numbers, which is the 2-rainbow independent dominating function (2RiDF) on graphs. The minimum weight of a 2RiDF on a graph <inline-formula> <tex-math notation="LaTeX">$G$ </tex-math></inline-formula> is called the <italic>2-rainbow independent domination number</italic> of <inline-formula> <tex-math notation="LaTeX">$G$ </tex-math></inline-formula>. A graph <inline-formula> <tex-math notation="LaTeX">$G$ </tex-math></inline-formula> is 2-rainbow independent domination stable if the 2-rainbow independent domination number of <inline-formula> <tex-math notation="LaTeX">$G$ </tex-math></inline-formula> remains unchanged under removal of any vertex. As a result, we characterize 2-rainbow independent domination stable tree-networks and study the effect of edge removal on 2-rainbow independent domination number in trees.

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