Bounds for fuzzy Zagreb Estrada index

Document Type : Original paper

Authors

1 NMIMS Deemed tobe University, Mumbai.

2 NMIMS Deemed to University

Abstract

Let $G(V,\sigma ,\mu )$ be a fuzzy graph of order $n$, where $\sigma(u)$ is the vertex membership, $\mu(u,v)$ is membership value of an edge and $\mu (u)$ is the strength of vertex. The first fuzzy Zagreb index is the sum $\sigma ({{u}_{i}})\mu ({{u}_{i}})+\sigma ({{u}_{j}})\mu ({{u}_{j}})$ where ${{{u}_{i}}{{u}_{j}}\in {{\mu }}}$ and the corresponding fuzzy Zagreb matrix is the square matrix of order $n$ whose $(i,j)^{th}$ entry whenever $i\neq j$, is $\sigma ({{u}_{i}})\mu ({{u}_{i}})+\sigma ({{u}_{j}})\mu ({{u}_{j}})$ and zero otherwise. In this paper, we introduce the Zagreb Estrada index of fuzzy graphs and establish some bounds for it.

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References

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Communications in Combinatorics and Optimization
Volume 8, Issue 1
March 2023
Pages 153-160

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