Regular Restrained Domination in Middle Graph

M.H.Muddebihal; ShobhaMahadevappa

Author(s)

M.H.Muddebihal Department of Mathematics, Gulbarga University,Kalaburagi-585106,

ShobhaMahadevappa Government First Grade College,Shahapur-585223,

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.

Publication Details

Page(s) 1558-1562

DOI DOI not available

Published Journal: International Journal of Membrane Science and Technology, Volume: 10, Issue: 1, Year: 2023

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Keywords

Graph, Regular Restrained Domination Number, Middle Graph, Restrained Dominating Set, dominating set

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