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On minimum intersections of certain secondary dominating sets in graphs

Kosiorowska Anna, Michalski Adrian, Włoch Iwona

Opuscula Mathematica

2023

Vol. 43, no. 6

813--827

In this paper we consider secondary dominating sets, also named as (1,k)-dominating sets, introduced by Hedetniemi et al. in 2008. In particular, we study intersections of the (1, 1)-dominating sets and proper (1, 2)-dominating sets. We introduce (1,2)-intersection index as the minimum possible cardinality of such intersection and determine its value for some classes of graphs.