Title: On independent domination topological indices of graphs

Authors: Anjaneyulu Mekala; U. Vijaya Chandra Kumar; R. Murali

Addresses: Department of Mathematics, Guru Nanak Institutions Technical Campus (Autonomous), Hyderabad, Telangana-501506, India ' School of Applied Sciences (Mathematics), REVA University, Bengaluru, Karnataka-560064, India ' Department of Mathematics, Dr. Ambedkar Institute of Technology, Bengaluru, Karnataka-560056, India

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 d_id(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.

Keywords: independent domination number; independent minimal dominating number; independent domination degree Zagreb indices.

DOI: 10.1504/IJMOR.2024.142449

International Journal of Mathematics in Operational Research, 2024 Vol.29 No.3, pp.345 - 353

Received: 17 Apr 2023
Accepted: 07 May 2023
Published online: 31 Oct 2024 *

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