Monomorphic domination integrity in fuzzy graphs

Articles in Press

Document Type : Research Paper

Authors

1 Department of Mathematics, Scott Christian College (Autonomous), Tamil Nadu, India,

2 Department of Mathematics, Scott Christian College (Autonomous),Tamil Nadu, India.

10.22098/jhs.2025.16407.1064

Abstract

Let M be a subset of V (G) and let G : (V, σ, μ) be a fuzzy graph. The mononphonic domination integrity (MDI) of G is defined by (MDI) ̃(G)^= min{|M|+m(G−M): M is a monophonic dominating set of G}, where |M|=∑_(u∈M)σ(u)and m(G − M) is the order of the greatest component of G−M. The notion of vulnerability parameter MDI in fuzzy graphs is presented in this work. Further, the MDI for complete fuzzy graph, complete bipartite fuzzy graph, join and cartesian product of two fuzzy graphs and bounds are also discussed. Also we present a decision-making problem involving the optimization of bus routes and the strategic placement of bus stations using MDI principles.

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References

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Journal of Hyperstructures

Articles in Press, Accepted Manuscript
Available Online from 17 June 2025

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