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Bounds on Doubly Connected Fair Dominations in Graphs
Abstract
. A dominating set π of graph π = (π, π) is a doubly connected fair dominating set (dcfd-set) if it satisfies the following conditions: (1) the induced subgraphs < π > and < π\π > are connected and (2) every vertex not in π are dominated by the equal number of vertices from π . The dcfd(G) is the minimum cardinality of a dcfd-set in π . In this paper, the doubly connected fair domination number, dcfd(G), of some standard graphs is given. Also, doubly connected fair domination number is related to other parameters. Moreover, Nordhaus-Gaddum-type results are found to be doubly connected fair domination number.