The strong metric dimension of generalized Sierpiński graphs with pendant vertices

Ehsan Estaji, Juan Alberto Rodríguez-Velázquez

Abstract


Let G be a connected graph of order n having ɛ(G) end-vertices. Given a positive integer t, we denote by S(G, t) the t-th generalized Sierpiński graph of G. In this note we show that if every internal vertex of G is a cut vertex, then the strong metric dimension of S(G, t) is given by dims(S(G, t)) = (ɛ(G)(nt − 2nt − 1 + 1) − n + 1) / (n − 1).


Keywords


Strong metric dimension, Sierpiński graphs

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ISSN: 1855-3974

Issues from Vol 6, No 1 onward are partially supported by the Slovenian Research Agency from the Call for co-financing of scientific periodical publications