Changing and Unchanging strong efficient edge domination number of some standard graphs when a vertex is removed or an edge is added

Authors

  • M Annapoopathi Department of Mathematics, P.G. & Research Department of Mathematics, The M.D.T. Hindu College, Tirunelveli. (Affiliated to Manonmaniam Sundaranar University, Tirunelveli – 627 012, Tamil Nadu, India) and Assistant Professor, National Engineering College, Kovilpatti - 628503, Tamil Nadu, India
  • N Meena Department of Mathematics, the M.D.T. Hindu College, Tirunelveli. (Affiliated to Manonmaniam Sundaranar University, Tirunelveli – 627 012, Tamil Nadu, India)

DOI:

https://doi.org/10.23755/rm.v45i0.1024

Keywords:

Domination, edge domination, strong edge domination, efficient edge domination, strong efficient edge domination

Abstract

Let G=(V,\ E) be a simple graph. A subset S of E(G) is a strong (weak) efficient edge dominating set of G if │Ns[e]  S│ = 1 for all e  E(G)(│Nw[e]  S│ = 1 for all e  E(G)) where Ns(e) ={f / f  E(G), f is adjacent to e & deg f ≥ deg e}(Nw(e) ={f / f  E(G), f is adjacent to e & deg f ≤ deg e}) and Ns[e]=Ns(e){e}(Nw[e] = Nw(e){e}). The minimum cardinality of a strong efficient edge dominating set of G (weak efficient edge dominating set of G) is called a strong efficient edge domination number of G and is denoted by {\gamma\prime}_{se}(G) ({\gamma^\prime}_{we}(G)).When a vertex is removed or an edge is added to the graph, the strong efficient edge domination number may or may not be changed. In this paper the change or unchanged of the strong efficient edge domination number of some standard graphs are determined, when a vertex is removed or an edge is added.

References

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Published

2023-01-30

Issue

Vol. 45 (2023): Special Issue: Advances in Applied and Intellectual Mathematics

Section

Volume 44-2022

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