Affiliation:
1. Department of Mathematics & Statistics Acadia University Wolfville Nova Scotia Canada
2. School of Mathematical and Computational Sciences University of Prince Edward Island Charlottetown Prince Edward Island Canada
Abstract
AbstractIn this paper we study the average order of dominating sets in a graph, . Like other average graph parameters, the extremal graphs are of interest. Beaton and Brown conjectured that for all graphs of order without isolated vertices, . Recently, Erey proved the conjecture for forests without isolated vertices. In this paper we prove the conjecture and classify which graphs have . We also use our bounds to prove an average version of Vizing's conjecture.
Funder
Natural Sciences and Engineering Research Council of Canada
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