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STRONG PERFECT NONBONDAGE NUMBER OF SOME GRAPHS

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Govindalakshmi T.S1*, Meena N2
» doi: 10.48047/ecb/2023.12.si10.00310

Abstract

Let G be a simple graph. A subset S  V(G) is called a strong (weak) perfect dominating set of G if |Ns(u) ∩ S| = 1(|Nw(u) ∩ S| = 1) for every u εV(G) - S where Ns(u) = {v ε V(G)/uv∈????(????), deg v ≥ deg u} (Nw(u) = {v εV(G)/uv∈????(????), deg v ≤ deg u}. The minimum cardinality of a strong (weak) perfect dominating set of G is called the strong (weak) perfect domination number of G and is denoted by γsp(G)(γwp(G)). The strong perfect non bondage number bspn(G) of a nonempty graph G is defined as the maximum cardinality among all sets of edges X ⊆ E(G) for which ????sp(G – X) =????sp(G). If bspn(G) does not exist, then bspn(G) is defined as zero. In this paper strong perfect nonbondage number of some standard graphs are determined.

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