Strongly Isolate Perfect Domination in Graphs

Authors

  • Sivagnanam Mutharasu Department of Mathematics, CBM College, India.
  • Sandhya S Department of Mathematics, CBM College, India.

DOI:

https://doi.org/10.63278/1480

Keywords:

Domination, isolate domination, strongly isolate perfect domination.

Abstract

A dominating set  of a graph  is said to be an isolate dominating set (IDS) if <  > has at least one isolated vertex. The ID number of  is represented by  . An ID-set  is considered as strongly isolate dominating set (SIDS) if there exists a ∈  such that   , where and . A dominating set  is called a perfect dominating set if every vertex in V (G) −  has exactly one neighbour in  . By using the above concept and the definition of SID, we define a new concept called  ”Strongly Isolate Perfect Domination”(SIPD). An isolate dominating set  is said to be strongly isolate perfect dominating set if there exists  such that  and  is a perfect dominating set of . This paper involves some basic features of SIPDS and compare SIPDS with dominating set, ID-set and efficient dominating set (EDS). At the end, includes SIPD number of path, cycle, complete bi- partite graph, complete b- partite graph and some group of graphs.

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Published

2025-04-16

How to Cite

Sivagnanam Mutharasu, and Sandhya S. 2025. “Strongly Isolate Perfect Domination in Graphs ”. Metallurgical and Materials Engineering 31 (4):524-28. https://doi.org/10.63278/1480.

Issue

Vol. 31 No. 4 (2025)

Section

Research

License

Copyright (c) 2025 Sivagnanam Mutharasu, Sandhya S

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