Published July 30, 2025 | Version CC-BY-NC-ND 4.0
Journal article Open

On Degree Dominating Functions in Graphs

Authors/Creators

  • 1. Department of Studies in Mathematics, Manasagangothri, University of Mysore, Mysuru (Karnataka), India.

Contributors

Contact person:

Researcher:

  • 1. Department of Studies in Mathematics, Manasagangothri, University of Mysore, Mysuru (Karnataka), India.

Description

Abstract: A set 𝑺 the number of vertices in a graph 𝑮 is said to be a dominating set if every vertex in 𝑽 − 𝑺 is adjacent to some vertex in 𝑺. A degree dominating function ( 𝑫𝑫𝑭 ) is a function 𝒇: 𝑽(𝑮) ∣ {𝟎, 𝟏, 𝟐, 𝟑, … ,𝜟(𝑮) + 𝟏} having the property that every vertex 𝒗 of 𝑺 is assigned with 𝒅𝒆𝒈(𝒗) + 𝟏 and all remaining vertices with zero. The weight of a degree dominating function 𝒇 is defined by 𝒘(𝒇) = ∑𝒗∈𝑺 (𝒅𝒆𝒈(𝒗) + 𝟏). The degree domination number, denoted by 𝜸deg (𝑮) is the minimum weight of all possible 𝑫𝑫𝑭𝒔. In this paper, we extended the study of the degree domination number of some classes of graphs.

Files

B825014020725.pdf

Files (606.5 kB)

Name Size Download all
md5:ee660d17fdb822595cc172b477330e9a
606.5 kB Preview Download

Additional details

Identifiers

DOI
10.35940/ijrte.B8250.14020725
EISSN
2277-3878

Dates

Accepted
2025-07-15
Manuscript received on 01 May 2025 | First Revised Manuscript received on 17 May 2025 | Second Revised Manuscript received on 01 July 2025 | Manuscript Accepted on 15 July 2025 | Manuscript published on 30 July 2025.

References

  • C. Berge: Theory of Graphs and its Applications, Methuen and Co.Ltd, London 1962. https://www.sciepub.com/reference/175421
  • N.C. Demirpolat, and E. Kilic, On Degree Domination in Graph, J. of Modern Technology and Eng. 9(2),(2024),112-118. DOI : https://doi.org/10.62476/jmte9112
  • M. Dinorog and I.S. Cabahug, Ring Domination Number of Some Mycielski Graphs, Asian Research J. of Mathematics, 18(12), (2022).
  • T. W. Haynes, S. T. Hedetniemi and P. J. Slater, "Fundamentals of domination in Graphs", Marcel Dekker, New-York 1998.
  • P. Mahalank, S.O. Yildirim, F.E. Zihni, B.K. Majni and I.N. Cangul, Some topological indices of Pentagonal Double chains, ITM Web of Conf. 49, 01004 (2022) Fourth ICAMNM 2022