On the existence and the number of independent (1,2)-dominating sets in the G-join of graphs

Adrian Michalski and Iwona Włoch

Applied Mathematics and Computation, 2020, vol. 377, issue C

Abstract: In 2008 Hedetniemi et al. introduced the concept of secondary dominating sets and pointed out that the problem of the existence of an independent (1,2)-set is NP-complete in the general case. In this paper we study independent (1,2)-dominating sets in certain classes of graphs. We give the complete characterization of G-join of graphs with an independent (1,2)-dominating set. Moreover, we determine the number of all independent (1,2)-dominating sets in the G-join of special factors using Padovan and Perrin numbers.

Keywords: Domination; Independence; G-join; Counting; Padovan numbers (search for similar items in EconPapers)
Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:377:y:2020:i:c:s0096300320301247

DOI: 10.1016/j.amc.2020.125155

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