A tight upper bound on the average order of dominating sets of a graph

Author:

Beaton Iain1ORCID,Cameron Ben2

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

Publisher

Wiley

Reference28 articles.

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4. On the mean order of connected induced subgraphs of block graphs;Balodis K. J.;Australas. J. Combin,2020

5. The average order of dominating sets of a graph;Beaton I.;Discrete Math,2021

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