Iterative Construction of the Minimum Independent Dominating Sets in Hypercube Graphs

An independent dominating set in a graph is a subset of vertices such that every vertex in a graph is either in the set or adjacent to a vertex in it, and no two vertices in the set are adjacent. An independent dominating set with the smallest cardinality is called the Minimum Independent Dominating Set (MIDS). Finding an MIDS in a graph is an NP-hard problem. In particular, this problem in hypercube graphs of dimension 2 k- 1 , k being a positive integer ≥ 1 , coincides with the problem of identifying an efficient dominating set in Cayley graphs. This work proposes a method employing non-recursive technique to solve the problem in hypercube graphs of dimension 2 k- 1 in exponential time. The work overcomes the limitation in the method given in the earlier paper of this author (Chowdhury, Debabani and Das, Debesh K. and Bhattacharya, Bhargab B. B. (2022) Improved Upper Bound on Independent Domination Number for Hypercubes. arXiv identifier 2205.06671). © 2022, The Author(s), under exclusive licence to Springer Nature Switzerland AG.