On Some Bounds of Fuzzy Secure Domination Number

Authors

  • Mariya C. Joy Centre for Post Graduate Studies and Research Department of Mathematics, Bharata Mata College, Thrikkakara, Kochi, Kerala, India https://orcid.org/0009-0002-4876-001X
  • Paul Isaac Centre for Post Graduate Studies and Research Department of Mathematics, Bharata Mata College, Thrikkakara, Kochi, Kerala, India https://orcid.org/0000-0002-4915-8525

DOI:

https://doi.org/10.26713/cma.v16i3.3205

Keywords:

Fuzzy graphs, Fuzzy secure domination, Fuzzy secure total domination, Fuzzy secure total domination number

Abstract

In a fuzzy graph \(G_f(\rho, \eta)\) with vertex set \(V\), a subset \(D \subseteq V\) is called a dominating set if each vertex in the graph is either a member of \(D\) or has at least one strong neighbor in \(D\). A secure dominating set \(S\) is a dominating set with the additional property that every vertex outside \(S\) has a strong neighbor in \(S\), that can swap places with it and still maintain domination. The minimum fuzzy cardinality of such secure dominating sets is called the secure domination number, denoted \(\gamma_{sc}(G_f)\). This paper explores bounds for the fuzzy secure domination number and examines its relationship with the domination number, independence number, and matching number.

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Published

30-10-2025
CITATION

How to Cite

Joy, M. C., & Isaac, P. (2025). On Some Bounds of Fuzzy Secure Domination Number. Communications in Mathematics and Applications, 16(3), 861–867. https://doi.org/10.26713/cma.v16i3.3205

Issue

Vol. 16 No. 3 (2025)

Section

Research Article

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