(G,D)-Bondage and (G,D)-Nonbondage Number of a Graph

S.Kalavathi; K.Palani

doi:https://doi.org/10.14445/22315373/IJMTT-V57P510

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 57 | Number 1 | Year 2018 | Article Id. IJMTT-V57P510 | DOI : https://doi.org/10.14445/22315373/IJMTT-V57P510

(G,D)-Bondage and (G,D)-Nonbondage Number of a Graph

S.Kalavathi, K.Palani

Citation :

S.Kalavathi, K.Palani, "(G,D)-Bondage and (G,D)-Nonbondage Number of a Graph," International Journal of Mathematics Trends and Technology (IJMTT), vol. 57, no. 1, pp. 67-72, 2018. Crossref, https://doi.org/10.14445/22315373/IJMTT-V57P510

Abstract

The (G,D)-bondage number of a graph G denoted by b𝛾𝐺 (𝐺) is the least positive integer k such that there exists 𝐹 ⊆ 𝐸(𝐺) with 𝐹 = 𝑘 and 𝛾𝐺 (𝐺 − 𝐹) > 𝛾𝐺 (𝐺). If no such k exists, it is defined to be ∞. The (G,D)-nonbondage number of a graph G denoted by bn𝛾𝐺 (𝐺) is defined as the maximum cardinality among all sets of edges 𝑋 ⊆ 𝐸(𝐺) such that 𝛾𝐺 𝐺 − 𝑋 = 𝛾𝐺 𝐺 . If bn𝛾𝐺 (𝐺)does not exist, we define bn𝛾𝐺 𝐺 = 0.In this paper we initiate a study of these two parameters.

Keywords

Domination, Geodomination, (G, D)-number, (G, D)-bondage number and (G, D)-nonbondage number.

References

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