Valency based domination number for Mycielskian of some graphs‎

Document Type : Original Article

Authors

Department of Mathematics, St. Mary's College(Autonomous), Thrissur, University of Calicut

Abstract
Let G = (V, E) be a connected graph and γvb(G) denotes the valency based domination number of G or simply vb-domination number of G. In this paper, analogous to isolated vertex in domination, defined valency based isolated vertex (or simply, vb-isolated vertex ) in vb-domination and proved that vb-isolated vertices belong to any vb-dominating set. Also studied its properties in the graph G as well as in its Mycielskian, µ(G). Established an inequality connecting vb-domination number of Mycielskian of G and domination number of G. Obatined an upper bound for vb-domination number of Mycielskian of regular
graphs. Also calculated vb-domination number of Mycielskian of some graph classes.

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Subjects


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Volume 6, Issue 4
Autumn 2025
Pages 33-43

  • Receive Date 18 October 2025
  • Revise Date 28 November 2025
  • Accept Date 04 December 2025