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- W2152918591 abstract "Let S be the set of minimal dominating sets of graph G and U, W ⊂ S with U S W = S and U T W = ∅. A Smarandachely mediate-(U, W ) dominating graph D S(G) of a graph G is a graph with V (D S(G)) = V ' = V S U and two vertices u, v ∈ Vare adjacent if they are not adjacent in G or v = D is a minimal dominating set containing u. particularly, if U = S and W = ∅, i.e., a Smarandachely mediate-(S, ∅) dominating graph D S(G) is called the mediate dominating graph Dm(G) of a graph G. In this paper, some necessary and sufficient conditions are given forDm(G) to be connected, Eulerian, complete graph, tree and cycle respectively. It is also shown that a given graph G is a mediate dominating graph Dm(G) of some graph. One related open problem is explored. Finally, some bounds on domination number of Dm(G) are obtained in terms of vertices and edges of G." @default.
- W2152918591 created "2016-06-24" @default.
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- W2152918591 date "2011-12-03" @default.
- W2152918591 modified "2023-09-28" @default.
- W2152918591 title "Mediate Dominating Graph of a Graph" @default.
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- W2152918591 doi "https://doi.org/10.5281/zenodo.9306" @default.
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