Regular Restrained Domination in Middle Graph

Authors

  • M.H. Muddebihal Department of Mathematics, Gulbarga University, Kalaburagi-585106.
  • Shobha Mahadevappa Government First Grade College, Shahapur-585223

DOI:

https://doi.org/10.15379/ijmst.v10i1.2988

Keywords:

Graph, Middle Graph, Dominating Set, Restrained Dominating Set, Regular Restrained Domination Number.

Abstract

In this paper, we introduce the new concept called regular restrained domination in middle graph.A set S ? V[M(G)] is a restrained dominating set if every vertex in V-S is adjacent to a vertex in S and another vertex in V-S. Note that every graph has a restrained dominating set, since S=V is such a set. Let  ?rr[M(G)] denote the size of a smallest restrained dominating set. Also we study the graph theoretic properties of ?rr[M(G)] and many bounds were obtained in terms of elements of G and its relationships with other domination parameters were found.

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Published

2023-11-01

How to Cite

[1]
M. Muddebihal and S. Mahadevappa, “Regular Restrained Domination in Middle Graph”, ijmst, vol. 10, no. 1, pp. 1558-1562, Nov. 2023.