Detour Certified Domination Number of Degree Splitting Graphs of Certain Graphs

Authors

  • Rashmi Carmel A, T. Muthu Nesa Beula

Keywords:

: Detour set, Dominating set, certified domination, Detour certified domination, Degree Splitting Graph

Abstract

In this paper, we introduce the concept detour certified domination number of a graph. Also detour certified domination number of a certain classes of graphs are determined and some of its general properties are studied. A set  of vertices in a connected graph  is called a detour set if every vertex not in  lies on a longest path between two vertices from . A set  of vertices in  is called a dominating set of  if every vertex not in  has at least one neighbour in . A set  is called a certified dominating set of  if  is a dominating set and every vertex in  has either zero or at least two neighbours in . A set  is called a detour certified dominating set of  if  is both detour and certified dominating set of . The detour certified domination number is the minimum cardinality of a detour certified dominating set in .

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References

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Published

23.12.2024

How to Cite

Rashmi Carmel A. (2024). Detour Certified Domination Number of Degree Splitting Graphs of Certain Graphs. International Journal of Intelligent Systems and Applications in Engineering, 12(4), 6061–6072. Retrieved from https://www.ijisae.org/index.php/IJISAE/article/view/8478

Issue

Vol. 12 No. 4 (2024)

Section

Research Article

License

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