Nonexistence of Efficient Dominating Sets in the Cayley Graphs Generated by Transposition Trees of Diameter 3
Abstract
Let d,n be positive integers such that d<n, and let Xdn be a Cayley graph generated by a transposition tree of diameter d. It is known that every Xdn with d<3 splits into efficient dominating sets. The main result of this paper is that X3n does not have efficient dominating sets.
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