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On independent domination topological indices of graphs

Author

Listed:
  • Anjaneyulu Mekala
  • U. Vijaya Chandra Kumar
  • R. Murali

Abstract

A dominating set (ds) D of a graph G = (V, E) is an independent dominating set (Ids), if the induces subgraph 〈D〉 has no edges. The independent domination number i(G) of graph G is the minimal cardinality of an Ids. In this paper we define a new independent degree domination (Idd) of each vertex k ∈ V(G), called an Idd of k and denoted by did(k) are introduced, as well as certain domination indices based on this Idd and also fundamental properties are investigated. We establish exact value for the Idd Zagreb indices of book graph, windmill graph, middle graph of cycle.

Suggested Citation

  • Anjaneyulu Mekala & U. Vijaya Chandra Kumar & R. Murali, 2024. "On independent domination topological indices of graphs," International Journal of Mathematics in Operational Research, Inderscience Enterprises Ltd, vol. 29(3), pages 345-353.
    • Handle: RePEc:ids:ijmore:v:29:y:2024:i:3:p:345-353
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