On Degree Dominating Functions in Graphs
V. Thukarama1, Soner N.D.2
1V. Thukarama, Department of Studies in Mathematics, Manasagangothri, University of Mysore, Mysuru (Karnataka), India.
2Soner N.D., Department of Studies in Mathematics, Manasagangothri, University of Mysore, Mysuru (Karnataka), India.
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 | PP: 20-22 | Volume-14 Issue-2, July 2025 | Retrieval Number: 100.1/ijrte.B825014020725 | DOI: 10.35940/ijrte.B8250.14020725
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© The Authors. Blue Eyes Intelligence Engineering and Sciences Publication (BEIESP). This is an open access article under the CC-BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/)
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.
Keywords: Domination Number, Degree Domination, Mycielski Graph, Pentagonal chain. AMS Subject Classification: 05C69, 05C76, 68R10.
Scope of the Article: Computer Science and Applications