Volume 27 , Issue 2 , PP: 167-174, 2026 | Cite this article as | XML | Html | PDF | Full Length Article
Aparna Tripathy 1 , Amaresh Chandra Panda 2 , Siva Prasad Behera 3 , Prasanta Kumar Raut 4 , Mana Donganont 5 * , Said Broumi 6
Doi: https://doi.org/10.54216/IJNS.270214
Average edge connectivity is a fundamental concept in graph theory, widely employed to evaluate the robustness of networks through the analysis of local edge cuts. Classical fuzzy extensions allow for graded membership, yet they fail to clearly distinguish between inherent uncertainty and definite absence of edges. To overcome this limitation, we introduce the notion of neutrosophic average edge connectivity, a tri-valued connectivity measure formulated within the framework of single-valued neutrosophic graphs (SVNGs). In this study, we rigorously define neutrosophic local edge cuts, establish key theoretical results including bounds and monotonicity properties, and design efficient algorithms tailored for particular families of graphs. The applicability of the proposed framework is demonstrated through a detailed communication-network case study, which highlights its capacity to capture structural resilience under indeterminate conditions. Overall, the proposed approach generalizes classical robustness indicators and provides a comprehensive tool for analyzing connectivity in networks characterized by vagueness, indeterminacy, and incomplete information.
Neutrosophic graph , Local edge cut , Average edge connectivity , Robustness , Communication networks
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