Neutrosophic Average Edge Connectivity with Applications to
Communication Networks
Aparna Tripathy1,˚, Amaresh Chandra Panda1, Siva Prasad Behera1, Prasanta Kumar Raut2,
Mana Donganont3, Said Broumi4
1Department of Mathematics, C.V. Raman Global University, Bhubaneswar, Odisha, India
2Department of Mathematics, Trident Academy of Technology, Bhubaneswar, Odisha, India
3Department of Mathematics, School of Science, University of Phayao, Phayao 56000, Thailand
4Laboratory of Information Processing, Faculty of Science Ben M’Sik, University of Hassan II, Casablanca,
Morocco
Emails: aparnatripathy03@gmail.com; amaresh.chandra.panda@cvrgi.edu.in; sivaiitkgp12@gmail.com;
prasantaraut95@gmail.com; mana.do@up.ac.th; broumisaid78@gmail.com
Abstract
Average edge connectivity is a fundamental concept in graph theory, widely employed to evaluate the ro-
bustness 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 ap-
plicability 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 pro-
posed approach generalizes classical robustness indicators and provides a comprehensive tool for analyzing
connectivity in networks characterized by vagueness, indeterminacy, and incomplete information.
Keywords: Neutrosophic graph; Local edge cut; Average edge connectivity; Robustness; Communication
networks