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Journal of Discrete Mathematical Sciences and Cryptography cover
Open Access ·Peer-reviewed·ISSN (Online): 2169-0065·ISSN (Print): 0972-0529

Monthly Journal: Publishes theoretical and applied research in all areas of Discrete Mathematical Sciences, Cryptography, Combinatorics, Elliptic Curves and Information Security.

Issues up to 2022 co-published with and available at:Taylor & Francis Online
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Open Access Research Article

Analyzing Δ(G) and δ(G) in graph theory for improved network analysis algorithms

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* Corresponding author · click or hover a name for details

pp. 289–297Vol. 29Issue 1January 2026DOI: 10.47974/JDMSC-2485 Crossmark XML
Received:
08 Apr 2025
Published Online:
31 Dec 2025
Article type:
Research Article
Language:
EN
Article no.:
JDMSC-2485
Pages:
289–297

Abstract

Graph theory has long been used to study complicated networks by focusing on building components like the highest and lowest degrees (u03a6(G)). The strength, connection, and vulnerability of a network rely on these two characteristics. The greatest number of edges reaching a vertex is Δ(G), whereas the smallest number connecting to it is ε(G). These numbers are vital to network analysis because they guarantee load sharing, resilience, and network optimization work. This paper explores the meaning of Δ(G) and ε(G) in advanced network analysis, using both theoretical and practical examples. We study how degree measurements might enhance fault-tolerant systems, routing methods, and network traffic analysis by creating more connected, less crowded networks. Additionally, we address existing methods and suggest alternate applications of Δ(G) and ε(G) to improve and speed network analysis. The study concludes by discussing how these measures may influence graph theory algorithm development.

Keywords

Subject Classifications

05C82

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