Abstract

In this paper, interesting results regarding the Mycielskian number of the Mycielski’s graph of path μ(Pn), the Mycielski’s graph of cycle μ(Cn), the Mycielski’s graph of complete graph μ(Kn), the Mycielski’s graph of complete bi-partite graph μ(Km,n), the Mycielski’s graph of wheel graph μ(Wn), the
Mycielski’s graph off an graph μ(F1,n), the Mycielski’s graph of tadpole graph μ(Tm,n), the Mycielski’s graph of snake graph μ(Tn) and the Mycielski’s graph of zero divisor graphsμ(Γ(Zn))under the domination parameters such as blast domination,distance-2 domination, blast distance-2 domination and independent distance-2 domination are investigated. The exact values of these new parameters for some special graphs are attained. The relation with other domination parameters have been discussed.

Keywords and Phrases

Blast domination number, Blast distance-2 domination number, Mycielski’s graph.

A.M.S. subject classification

05C76, 05C69.

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