On average lower independence and domination numbers in graphs

The average lower independence number i(av)(G) of a graph G=(V, E) is defined as 1/vertical bar V vertical bar Sigma(upsilon is an element of nu)i(upsilon)(G), and the average lower domination number gamma(av)(G) is defined as 1/vertical bar V vertical bar Sigma(upsilon is an element of nu)gamma(upsilon)(G), where i(upsilon)(G) (resp. gamma(upsilon) (G)) is the minimum cardinality of a maximal independent set (resp. dominating set) that contains upsilon. We give an upper bound of i(av) (G) and y(av) (G) for arbitrary graphs. Then we characterize the graphs achieving this upper bound for iav and for gamma(av) respectively. (c) 2005 Elsevier B.V. All rights reserved.