Total Equitable Bondage Number of a Graph

Authors

  • S. K. Vaidya Department of Mathematics Saurashtra University Rajkot-360 005 Gujarat India http://orcid.org/0000-0002-5394-1424
  • A. D. Parmar Atmiya Institute of Technology & Science for Diploma Studies, Rajkot - 360005 Gujarat India

DOI:

https://doi.org/10.3329/jsr.v10i3.33940

Keywords:

Dominating set, Equitable dominating set, Total dominating set, Bondage number.

Abstract

If for any total dominating set D with ν ∈ V (G) − D there exists a vertex u ∈ D such that uν ∈ E (G) and |d(ν)−d(u)| ≤ 1 then D is called the total equitable dominating set. The minimum cardinality of the total equitable dominating set is called the total equitable domination number denoted by γet (G). The bondage number b(G) of a nonempty graph G is the minimum cardinality among all sets of edges E0 ⊆ E(G) for which γ(G – E0) > γ(G). We introduced the concept of total equitable bondage number and proved several results.

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Author Biographies

S. K. Vaidya, Department of Mathematics Saurashtra University Rajkot-360 005 Gujarat India

Professor

Deapartment of Mathematics

A. D. Parmar, Atmiya Institute of Technology & Science for Diploma Studies, Rajkot - 360005 Gujarat India

Lecturer in Mathematics

Atmiya Institute of Technology & Science for Diploma Studies,
Rajkot - 360005
Gujarat
India

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Published

2018-09-01

How to Cite

Vaidya, S. K., & Parmar, A. D. (2018). Total Equitable Bondage Number of a Graph. Journal of Scientific Research, 10(3), 231–238. https://doi.org/10.3329/jsr.v10i3.33940

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Section

Section A: Physical and Mathematical Sciences