Strong sum 𝒅𝒅 distance - 𝒅𝒔𝒔𝒅 in fuzzy graphs

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Document Type : Research Paper

Authors

1 ms university (department of mathematics st.jude's college thoothoor)

2 St. Judes College, Thoothoor

Abstract

Abstract. For any connected Fuzzy graph G: (V, σ, μ), the strong sum distance between x and y is defined as 𝑑𝑠𝑠𝑑(x, y) = min {L(𝑃𝑠)} where 𝑃𝑠 is the strong x-y path. For any two vertices x and y of a graph G, 𝑑𝑑- distance is defined by considering the degrees of x and y along with the length of the path. In this paper we introduced strong sum 𝑑𝑑 distance in fuzzy graphs by considering distance as strong sum distance and degree of vertex as the sum of membership values of all edges which are incident at that vertex. We study some properties with this new distance. First we prove that the new distance is a metric on the set of vertices of G. Some properties of strong neighbors and eccentric nodes are obtained.

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References

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Journal of Hyperstructures

Articles in Press, Accepted Manuscript
Available Online from 20 June 2026

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